Workbook in Matlh Fourth

1WORKBOOK

IN MATHEMATICSVI

( fourth Quarter )

May Ester M. Rubio

Master Teacher I

1

WORKBOOK

IN MATHEMATICSVI

( fourth Quarter )

May Ester M. Rubio

Master Teacher I

1

WORKBOOK

IN MATHEMATICSVI

( fourth Quarter )

May Ester M. Rubio

Master Teacher I

1

WORKBOOK

IN MATHEMATICSVI

( fourth Quarter )

May Ester M. Rubio

Master Teacher I

2Chapter 14

PlaneFigures

Lesson No. 1 Polygons

Lesson No. 2 Area of Polygons

Lesson No. 1

Polygons2

Chapter 14

PlaneFigures



Lesson No. 1

Polygons2

Chapter 14

PlaneFigures



Lesson No. 1

Polygons2

Chapter 14

PlaneFigures



Lesson No. 1

Polygons

3Polygon is a simple closed curve formed by line segments with

common endpoints. The line segments are called sides, while the endpoints arecalled vertices. The name of the polygon indicates how many sides and howmany angle it has.

Regular polygon has all sides and all angles congruent.

Kinds of Polygon

1.Circle is a plane curve all points of which are equidistant from a pointcalled the center.

Parts of a Circle1. Radius is the distance from the center to the point on the circle2. Diameter is the distance from one point to another point on the circle

passing through the center.3. Chord a line segment whose endpoints are on the circle.

radius

diameter

chord

center

Circumference is the total length around the circle.

Pi ( ) is the ratio of the circumference to the diameter

- 3.14

2.Triangle a polygon that has three sides

- the sum of the angles of any triangle is 180

Classification of Triangle According to the Measure of their Angles:

1) right triangle a triangle that has one right angle.

2) acute triangle a triangle with three acute angles

3) Obtuse triangle a triangle with one obtuse angle.

Classification of Triangle According to the Measures of their Sides

1) Equilateral triangle a triangle with three congruent sides

42) Isosceles triangle a triangle with two equal sides.

3) Scalene triangle a triangle with no two sides of the same length

3.Quadrilateral is a polygon with four sides

a) Parallelogram has two pairs of opposite sides equal and parallel

b) Rhombus has four sides equal and two pairs of opposite sides parallel

c) Rectangle has two pairs of opposite sides equal and parallel andadjacent sides that are perpendicular

d) Square has four equal sides , two pairs of opposite sides parallel andperpendicular adjacent sides.

e) Trapezoid has only one pair of opposite sides parallel

4) Pentagon a polygon with five sides

5)Hexagon a polygon with six sides

6) Heptagon a polygon with seven sides

57) Octagon a polygon with eight sides

8) Nonagon a polygon with nine sides

9) Decagon a polygon with ten sides

Activity No. 1Write the letter of the correct answer.

_____ 1. A line segment with both endpoints on the circle.

_____ 2. The distance around the circle.

_____ 3. The ratio of the circumference to the diameter of a circle.

_____ 4. A line segment passing through the center with both endpoints on the

circle.

_____ 5. A figure formed by endpoints that are the same distance from a center

point.

Activity No. 2Study the circle and name the following line segments.

radius

diameter

chord

1) RT _____________________ 6) SO _____________________2) RP _____________________ 7) OQ _____________________

a) Diameter c) circumference e)b) Circle d) chord

5









circle.


point.


radius

diameter

chord

1) RT _____________________ 6) SO _____________________2) RP _____________________ 7) OQ _____________________


5









circle.


point.


radius

diameter

chord

1) RT _____________________ 6) SO _____________________2) RP _____________________ 7) OQ _____________________


5









circle.


point.


radius

diameter

chord

1) RT _____________________ 6) SO _____________________2) RP _____________________ 7) OQ _____________________


63) SU _____________________ 8) QT _____________________4) OU _____________________ 9) OR _____________________5) QP _____________________ 10) OT _____________________

Activity No. 3Identify the terms described in the following. Choose your answer inside thebox.

_______________ 1. has two pairs of opposite sides equal and parallel and

adjacent sides that are perpendicular

_______________ 2. has four equal sides , two pairs of opposite sides parallel

and perpendicular adjacent sides.

_______________ 3. a polygon with seven sides

_______________ 4. A kind of quadrilateral which has only one pair of opposite

sides parallel

_______________ 5. is a plane curve all points of which are equidistant from a

point called the center.

_______________ 6. A polygon with eight sides.

_______________ 7. A polygon with five sides.

_______________ 8. A polygon with three sides.

_______________ 9. A polygon with ten sides

_______________ 10. A polygon with six sides

Activity No. 4Identify the kind of triangle according to the measure of their sides.

Circle triangle square hexagon decagon

Rectangle pentagon trapezoid octagon heptagon

6

3) SU _____________________ 8) QT _____________________4) OU _____________________ 9) OR _____________________5) QP _____________________ 10) OT _____________________








sides parallel











6

3) SU _____________________ 8) QT _____________________4) OU _____________________ 9) OR _____________________5) QP _____________________ 10) OT _____________________








sides parallel











6

3) SU _____________________ 8) QT _____________________4) OU _____________________ 9) OR _____________________5) QP _____________________ 10) OT _____________________








sides parallel











71)_________________ 2)___________________3)_______________

4) ___________________ 5) _______________________

Activity No. 5Identify the kind of triangle according to their angles.

1) ________________2)___________________ 3)___________________

4) ____________________ 5) ______________________

Activity No. 6Count the number of sides to be able to identify the polygon.

7

1)_________________ 2)___________________3)_______________

4) ___________________ 5) _______________________


1) ________________2)___________________ 3)___________________

4) ____________________ 5) ______________________


7

1)_________________ 2)___________________3)_______________

4) ___________________ 5) _______________________


1) ________________2)___________________ 3)___________________

4) ____________________ 5) ______________________


7

1)_________________ 2)___________________3)_______________

4) ___________________ 5) _______________________


1) ________________2)___________________ 3)___________________

4) ____________________ 5) ______________________


81)___________________ 2)____________________3) __________________

4) ___________________ 5)____________________6)___________________

7)__________________ 8) ____________________ 9) _________________

10) ____________________________

Lesson No. 2

Area of Polygons8

1)___________________ 2)____________________3) __________________

4) ___________________ 5)____________________6)___________________

7)__________________ 8) ____________________ 9) _________________

10) ____________________________

Lesson No. 2

Area of Polygons8

1)___________________ 2)____________________3) __________________

4) ___________________ 5)____________________6)___________________

7)__________________ 8) ____________________ 9) _________________

10) ____________________________

Lesson No. 2

Area of Polygons8

1)___________________ 2)____________________3) __________________

4) ___________________ 5)____________________6)___________________

7)__________________ 8) ____________________ 9) _________________

10) ____________________________

Lesson No. 2

Area of Polygons

9Area is the number of square units contained in afigure. Study the figure below. Count the square units tobe able to find the area of the figure. What is the area ofthe figure ? _____________

To measure the area of polygon, the unit we use is in terms of squares.

Example: square centimeters cm2 or square meters m2

Area of Polygons1)Square A = s2

Example: A = s2

3cm = 3cm X 3cm

= 9 cm2

PracticeFind the area of the square.

1) 4.5cm 4) 1.6 m

2) 5)7 cm 12 m

3) 3.4 cm

2)Rectangle A = l X w

Example: A = l X w

9

Area is the number of square units contained in afigure. Study the figure below. Count the square units tobe able to find the area of the figure. What is the area ofthe figure ? _____________




Example: A = s2

3cm = 3cm X 3cm

= 9 cm2


1) 4.5cm 4) 1.6 m

2) 5)7 cm 12 m

3) 3.4 cm


Example: A = l X w

9





Example: A = s2

3cm = 3cm X 3cm

= 9 cm2


1) 4.5cm 4) 1.6 m

2) 5)7 cm 12 m

3) 3.4 cm


Example: A = l X w

9





Example: A = s2

3cm = 3cm X 3cm

= 9 cm2


1) 4.5cm 4) 1.6 m

2) 5)7 cm 12 m

3) 3.4 cm


Example: A = l X w

10

2 cm = 5 cm X 2 cm

= 10 cm2

5 cm

PracticeFind the area of the rectangle.

1) 2)3.5 cm 1.2 m

9 cm 7.5 m

3) 4)2.5 cm 4 m

6 cm 8 m

5)1.5 cm

3 cm

3)Parallelogram A = b X h

Example: A = b X h

3 cm = 3 cm X 4 cm

= 12 cm2

4 cm

PracticeFind the area of the parallelogram.

1) 2)2.4 cm 3.2 cm

10

2 cm = 5 cm X 2 cm

= 10 cm2

5 cm


1) 2)3.5 cm 1.2 m

9 cm 7.5 m

3) 4)2.5 cm 4 m

6 cm 8 m

5)1.5 cm

3 cm


Example: A = b X h

3 cm = 3 cm X 4 cm

= 12 cm2

4 cm


1) 2)2.4 cm 3.2 cm

10

2 cm = 5 cm X 2 cm

= 10 cm2

5 cm


1) 2)3.5 cm 1.2 m

9 cm 7.5 m

3) 4)2.5 cm 4 m

6 cm 8 m

5)1.5 cm

3 cm


Example: A = b X h

3 cm = 3 cm X 4 cm

= 12 cm2

4 cm


1) 2)2.4 cm 3.2 cm

10

2 cm = 5 cm X 2 cm

= 10 cm2

5 cm


1) 2)3.5 cm 1.2 m

9 cm 7.5 m

3) 4)2.5 cm 4 m

6 cm 8 m

5)1.5 cm

3 cm


Example: A = b X h

3 cm = 3 cm X 4 cm

= 12 cm2

4 cm


1) 2)2.4 cm 3.2 cm

11

5 cm 6 cm

3) 4)1.9 m 11 cm

8 m 16 cm

5)5.5 m

10 m

4)Trapezoid A = (b1 + b2) X h2

Example: b1 - 2 cm A = ( b1 + b2 ) X h2

= ( 2 cm + 6 cm) X 3 cmh 3 cm 2

= 8 cm X 3 cm2

b2 - 6 cm = 24 cm22

= 12 cm2

PracticeFind the area of the trapezoid.

1) 2.8 m 2) 3.6 cm

5 m 6cm

9 m 12 cm

3) 4 cm 4) 7 cm

4.25 cm 5.5cm

8.5 cm 10 cm5) 8 m

3.5 m

10.5 m

11

5 cm 6 cm

3) 4)1.9 m 11 cm

8 m 16 cm

5)5.5 m

10 m



= ( 2 cm + 6 cm) X 3 cmh 3 cm 2

= 8 cm X 3 cm2

b2 - 6 cm = 24 cm22

= 12 cm2


1) 2.8 m 2) 3.6 cm

5 m 6cm

9 m 12 cm

3) 4 cm 4) 7 cm

4.25 cm 5.5cm

8.5 cm 10 cm5) 8 m

3.5 m

10.5 m

11

5 cm 6 cm

3) 4)1.9 m 11 cm

8 m 16 cm

5)5.5 m

10 m



= ( 2 cm + 6 cm) X 3 cmh 3 cm 2

= 8 cm X 3 cm2

b2 - 6 cm = 24 cm22

= 12 cm2


1) 2.8 m 2) 3.6 cm

5 m 6cm

9 m 12 cm

3) 4 cm 4) 7 cm

4.25 cm 5.5cm

8.5 cm 10 cm5) 8 m

3.5 m

10.5 m

11

5 cm 6 cm

3) 4)1.9 m 11 cm

8 m 16 cm

5)5.5 m

10 m



= ( 2 cm + 6 cm) X 3 cmh 3 cm 2

= 8 cm X 3 cm2

b2 - 6 cm = 24 cm22

= 12 cm2


1) 2.8 m 2) 3.6 cm

5 m 6cm

9 m 12 cm

3) 4 cm 4) 7 cm

4.25 cm 5.5cm

8.5 cm 10 cm5) 8 m

3.5 m

10.5 m

12

5)Triangle A = b X h2

Example: A = b X h2

h 3 cm = 3 cm X 6 cm2

= 18 cm2b - 6 cm 2

= 9 cm2

PracticeFind the area of the following triangles.

1) 2) 3)6 cm 8 cm 4.5cm

12 cm 15 cm 25 cm

4) 5)

7.5 m 9 m

11.5 m 7 m

6)Circle

Example:= 3.14 X ( 3 cm ) 2= 3.14 X 9 cm 2

r 3 cm = 28.26 cm2

12


Example: A = b X h2

h 3 cm = 3 cm X 6 cm2

= 18 cm2b - 6 cm 2

= 9 cm2


1) 2) 3)6 cm 8 cm 4.5cm

12 cm 15 cm 25 cm

4) 5)

7.5 m 9 m

11.5 m 7 m

6)Circle

Example:= 3.14 X ( 3 cm ) 2= 3.14 X 9 cm 2

r 3 cm = 28.26 cm2

12


Example: A = b X h2

h 3 cm = 3 cm X 6 cm2

= 18 cm2b - 6 cm 2

= 9 cm2


1) 2) 3)6 cm 8 cm 4.5cm

12 cm 15 cm 25 cm

4) 5)

7.5 m 9 m

11.5 m 7 m

6)Circle

Example:= 3.14 X ( 3 cm ) 2= 3.14 X 9 cm 2

r 3 cm = 28.26 cm2

12


Example: A = b X h2

h 3 cm = 3 cm X 6 cm2

= 18 cm2b - 6 cm 2

= 9 cm2


1) 2) 3)6 cm 8 cm 4.5cm

12 cm 15 cm 25 cm

4) 5)

7.5 m 9 m

11.5 m 7 m

6)Circle

Example:= 3.14 X ( 3 cm ) 2= 3.14 X 9 cm 2

r 3 cm = 28.26 cm2

13

PracticeFind the area of the following circles.

1) 2) 3)

4) 5)

Activity No. 7Compute the area of the following polygons.

1) 2)8 mm

9 cm12 mm

14 cm

3) 7 cm 4)

6 cm

10 cm

5) 6)

5 cm

12 cm

7) 8)

18 cm 5.25 m 10 m

8 cm36 cm

r 4 cm

8 cm

3.5 cm2.5 cm

13


1) 2) 3)

4) 5)


1) 2)8 mm

9 cm12 mm

14 cm

3) 7 cm 4)

6 cm

10 cm

5) 6)

5 cm

12 cm

7) 8)

18 cm 5.25 m 10 m

8 cm36 cm

r 4 cm

8 cm

3.5 cm2.5 cm

13


1) 2) 3)

4) 5)


1) 2)8 mm

9 cm12 mm

14 cm

3) 7 cm 4)

6 cm

10 cm

5) 6)

5 cm

12 cm

7) 8)

18 cm 5.25 m 10 m

8 cm36 cm

r 4 cm

8 cm

3.5 cm2.5 cm

13


1) 2) 3)

4) 5)


1) 2)8 mm

9 cm12 mm

14 cm

3) 7 cm 4)

6 cm

10 cm

5) 6)

5 cm

12 cm

7) 8)

18 cm 5.25 m 10 m

8 cm36 cm

r 4 cm

8 cm

3.5 cm2.5 cm

14

6 cm

9) 10) 21 cm

7 cm

Activity No. 8Solve for the area of the given polygons with their respective dimensions. Besure to use the correct unit.

1. SquareS = 11 cm

2. RectangleL = 8.5 mm ; w = 5 mm

3. Parallelogramb = 12.2 m ; h = 7.3 m

4. Right triangleL 8.5 mm ; h 7.46 m

5. Trapezoidb1 15 m ; b2 12.5 mh 7.2 m

6. Isosceles triangleb 17.4 dm ; h 11.2 dm

7. Rhombuss 15.5 m

8. Circler 8.5 cm

9. Circled 12.24 km

r - 6 cm11 cm

14

6 cm

9) 10) 21 cm

7 cm


1. SquareS = 11 cm






7. Rhombuss 15.5 m

8. Circler 8.5 cm

9. Circled 12.24 km

r - 6 cm11 cm

14

6 cm

9) 10) 21 cm

7 cm


1. SquareS = 11 cm






7. Rhombuss 15.5 m

8. Circler 8.5 cm

9. Circled 12.24 km

r - 6 cm11 cm

14

6 cm

9) 10) 21 cm

7 cm


1. SquareS = 11 cm






7. Rhombuss 15.5 m

8. Circler 8.5 cm

9. Circled 12.24 km

r - 6 cm11 cm

15

10.Trapezoidb1 2.5 m ; b2 9.75 mh 4.5 m

Activity No. 9

Solve the following problems.

1. A manila paper measures 102 cm and 57 cm. What is its area ?

2. Whose bedroom is bigger, Maria whose bedroom is 5 meters long and 4meters wide or Ana whose bedroom is 6 meters long and 3 meters wide ?Explain your answer.

3. A scarf has a base of 72 cm and an altitude of 33 cm. What is its area ?

4. A cake has a radius of 14 cm. What is the area of the cake ?

5. A lot trapezoidal in shape has an altitude of 4 meters. The first basemeasures 3.5 meters and the second base measures 4.3 meters. What isthe area of this lot ?

6. A lot is 40 cm by 36 cm. A house 27 m by 9 m is built on the lot. Howmuch area is left over ?

15


Activity No. 9








15


Activity No. 9








15


Activity No. 9








16

7. A standard sheet of typewriter paper is 21.6 cm by 27.9 cm. We usuallytype on a 16.5 cm by 22.9 cm area of the paper. What would be the areaof the margin ?

8. A lot is 36 m by 24 m. A triangular swimming pool with a height of 4.6 mand a base of 5.2 m is constructed on the lot. How much area is left over ?

9. The area of a parallelogram is 112.48 square cm, and the base is 15.2cm. Find the altitude.

10.Find the side of a square equal to a rectangle whose dimension are 32mand 72m.

11.Find the area of a rhombus whose diagonals are 24 and 30.

12.The ratio between the base and the altitude of a triangle is 2 : 3. If thearea of the triangle is 108 square cm, find the base.

13.The area of a trapezoid is 55 square m. The bases are 14 m and 8 m.Find the altitude.

14.The area and circumference of a circle are numerically equal. Find theradius.

17

15.Find the altitude of an isosceles triangle whose base is 8 cm and whoselegs are 5 cm.

16.The area of a parallelogram is 48 cm2. If its base is 12 cm, what is itsheight ?

17.The area of another parallelogram is 125 mm2 . If its height is 5 mm, whatis its base ?

18.The bases of a trapezoid are 18 cm and 12 cm. If its area is 210 cm2 ,what is its height ?

19.The perimeter of a square is 1.44 m. What is its area ?

20.A circular pool has a circumference of 81.64 m. What is the area of thepool ?

21.A square lot that measures 18.6 m on each side is for sale at Php 1,645per square meter. How much should be paid for the lot ?

22.Which is larger: a rectangular lot that measures 24 m by 18 m or a squarefield that measures 21 m on each side ?

18

23.Mrs. Reyes wants to order a rug for her dining room. She likes a round rugthat measures 2.75 m across. If each square meter of rug costs Php 824,how much would the rug cost ?

24.A bathroom floor that measures 3.6 m by 4.32 m will be covered with tiles,each measuring 15 cm b 15 cm. How many tiles will be needed ?

25.Which will need more fencing materials : a square field whose side is 50 mor a rectangular field which is 60 m long and 30 m wide ?

26.Two triangles have an equal area of 760 cm2. If the first triangle has abase of 40 cm and the second triangle has a base of 45 cm , which of thetwo triangles is taller ? by how much ?

27.A dog is tied loosely to a pole by a chain which is 2.7 m long. If he goesaround the pole once , what is the longest distance the dog can travel ?

28.Mr. Paredes has two lots. One is a rectangular lot that is 34 m long and 28m wide, while another is a square lot that measures 31 m on each side.How much would he get if he sold the two lots at Php 2,650 per squaremeter ?

29.What is the area of a lot with a length of 60 m and width of 36 m ?

19

30.The playground is 85 m long and 65 m wide. Find its area .

Chapter 1519


Chapter 1519


Chapter 1519


Chapter 15

20

SpatialFigures

Lesson No. 1 Spatial FiguresLesson No. 2 Surface AreaLesson No. 3 Volume

Lesson No. 1

Spatial FiguresSpatial figure or solid has 3 dimensions. It has length, width and height.

Observe the following solids. Find out what plane figures make up their faces.

a) Rectangular prism f) cone

20

SpatialFigures


Lesson No. 1




20

SpatialFigures


Lesson No. 1




20

SpatialFigures


Lesson No. 1




21

b) Triangular prism g) square pyramid

c) Hexagonal prism h) triangular pyramid

d) Cube i) sphere

e) cylinder

Activity No. 1Complete the table.

Solids

Numberof

Faces

Solids with polygon as facesSolids with circlesand polygons for

faces

square rectangle triangleOther

polygon Circles OthersABCD

21



d) Cube i) sphere

e) cylinder


Solids

Numberof

Faces


faces



21



d) Cube i) sphere

e) cylinder


Solids

Numberof

Faces


faces



21



d) Cube i) sphere

e) cylinder


Solids

Numberof

Faces


faces



22

EFGHI

Spatial Figures1) Prism a solid that has two bases that are congruent polygons lying in

parallel planes.The prism is named by the shape of its bases.a) Rectangular prism

b) Triangular prism

c) Hexagonal prism

2) Pyramid is a solid figure with a single base. The base is a polygonand the other faces are triangles.Example:

Square pyramid has a square base and four triangular faces.

Triangular pyramid with triangular base and 3 triangular faces.

3) Cylinder is a solid figure that has two circular bases that arecongruent and lie in parallel planes. It has one curved face which isactually a rectangle when cut and opened.

23

4) Cone is a solid figure that has a circular base and one vertex.

5) Sphere is a solid figure which has a surface that has always the samedistance from its center.

Activity No. 2Name the spatial figure of the following objects.

1. _________________________ 2. ________________________

3._____________________________ 4._________________________

5.____________________________ 6._________________________

23




1. _________________________ 2. ________________________

3._____________________________ 4._________________________

5.____________________________ 6._________________________

23




1. _________________________ 2. ________________________

3._____________________________ 4._________________________

5.____________________________ 6._________________________

23




1. _________________________ 2. ________________________

3._____________________________ 4._________________________

5.____________________________ 6._________________________

24

7.____________________________ 8._________________________

9.____________________________ 10.________________________

Lesson No. 2

Surface areaSurface Area ( SA ) is the sum of the areas of all the faces of a spatial figure.

The unit used is a square unit.

Finding the SA1. Cube

To find the SA of a cube, multiply the area of one face by 6.

24

7.____________________________ 8._________________________

9.____________________________ 10.________________________

Lesson No. 2





24

7.____________________________ 8._________________________

9.____________________________ 10.________________________

Lesson No. 2





24

7.____________________________ 8._________________________

9.____________________________ 10.________________________

Lesson No. 2





25

Example: A of Face = s2= 2 X 2= 4 m2

SA Cube = s2 X 6= 4 m2 X 6= 24 m2

PracticeFind the surface area of the cube.

1.

2.

3.

4.

5.

2. PrismIn finding the SA of other regular prisms, solve for the area of oneof the parallel and congruent bases and multiply it by 2 and thenfind the area of 1 of the rectangular faces and multiply this by thenumber of faces.

a) Rectangular prism

2cm

The rectangular prism has 6 faces:

2 m

5 cm

11 m

9 c m

1.5 m

4.5 m

5 cm4 cm

25


SA Cube = s2 X 6= 4 m2 X 6= 24 m2


1.

2.

3.

4.

5.



2cm


2 m

5 cm

11 m

9 c m

1.5 m

4.5 m

5 cm4 cm

25


SA Cube = s2 X 6= 4 m2 X 6= 24 m2


1.

2.

3.

4.

5.



2cm


2 m

5 cm

11 m

9 c m

1.5 m

4.5 m

5 cm4 cm

25


SA Cube = s2 X 6= 4 m2 X 6= 24 m2


1.

2.

3.

4.

5.



2cm


2 m

5 cm

11 m

9 c m

1.5 m

4.5 m

5 cm4 cm

26

There are 4 lateral faces (LA) and 2 bases ( BA)

4cm

2cm

Compute the area of the lateral face and the base

LA = l X w BA = l X w= 5 cm X 4 cm = 2 cm X 4 cm= 20 cm2 = 8 cm2

Multiply the LA by the number of lateral faces and the BA by the number of base.

SA rectangular prism = LA X 4 + BA X 2= 20 cm2 X 4 + 8 cm2 X 2= 80 cm2 + 16 cm2= 96 cm2

b) Triangular prism6 cm

2 cm

3 cmThe triangular prism has 5 faces.There are 3 rectangle which are the lateral faces and 2 triangle which are thebase.

2 cm

3 cm

Get the area of the rectangle and the triangle.

LA = l X w BA = b X h= 6 cm X 2 cm 2= 12 cm2 = 3 cm X 2 cm

2= 6 cm2 2= 3 cm2

Multiply the LA by the number of lateral faces and the BA by the number of base.

SA Triangular Prism = LA X 3 + BA X 2= 12 cm2 X 3 + 3 cm2 X 2= 36 cm2 + 6 cm2

4 cm5 cm

6 cm2 cm

27

= 42 cm2

PracticeFind the surface area of the following prism.

1) 8 cm

3 cm2 cm

2) 5 cm

4 cm

3 cm

3) 7 cm

6 cm

4 cm

4) 12 cm

5 cm

6 cm

5) 8 cm

7 cm

5 cm

3.CylinderCylinder has 3 faces. There are 2 circular base and 1 rectangular lateralface.

5 cm

2 cm

Get the area of the circular base and the area of the lateral face.

BA = r22 cm

27

= 42 cm2


1) 8 cm

3 cm2 cm

2) 5 cm

4 cm

3 cm

3) 7 cm

6 cm

4 cm

4) 12 cm

5 cm

6 cm

5) 8 cm

7 cm

5 cm


5 cm

2 cm


BA = r22 cm

27

= 42 cm2


1) 8 cm

3 cm2 cm

2) 5 cm

4 cm

3 cm

3) 7 cm

6 cm

4 cm

4) 12 cm

5 cm

6 cm

5) 8 cm

7 cm

5 cm


5 cm

2 cm


BA = r22 cm

27

= 42 cm2


1) 8 cm

3 cm2 cm

2) 5 cm

4 cm

3 cm

3) 7 cm

6 cm

4 cm

4) 12 cm

5 cm

6 cm

5) 8 cm

7 cm

5 cm


5 cm

2 cm


BA = r22 cm

28

= 3.14 X ( 2 ) 2= 3.14 X 4= 12.56 cm2

LA = 2 r X h= (2)(3.14) X (2 cm) X ( 5 cm)

5 cm = (6.28 cm)(2 cm) X ( 5 cm)= 62.8 cm2

Get the surface area of the cylinder.

SA cylinder = LA + (BA X 2 )= 62.8 cm2 + ( 12.56 cm2 X 2 )= 87.92 cm2

PracticeFind the surface area of the following cylinders.

1) 4 cm

9 cm

2) 14 cm

6 cm

3) 3 cm

12 cm4) 2 cm

3 cm

5)3.5 m

1.5 m

28

= 3.14 X ( 2 ) 2= 3.14 X 4= 12.56 cm2

LA = 2 r X h= (2)(3.14) X (2 cm) X ( 5 cm)

5 cm = (6.28 cm)(2 cm) X ( 5 cm)= 62.8 cm2




1) 4 cm

9 cm

2) 14 cm

6 cm

3) 3 cm

12 cm4) 2 cm

3 cm

5)3.5 m

1.5 m

28

= 3.14 X ( 2 ) 2= 3.14 X 4= 12.56 cm2

LA = 2 r X h= (2)(3.14) X (2 cm) X ( 5 cm)

5 cm = (6.28 cm)(2 cm) X ( 5 cm)= 62.8 cm2




1) 4 cm

9 cm

2) 14 cm

6 cm

3) 3 cm

12 cm4) 2 cm

3 cm

5)3.5 m

1.5 m

28

= 3.14 X ( 2 ) 2= 3.14 X 4= 12.56 cm2

LA = 2 r X h= (2)(3.14) X (2 cm) X ( 5 cm)

5 cm = (6.28 cm)(2 cm) X ( 5 cm)= 62.8 cm2




1) 4 cm

9 cm

2) 14 cm

6 cm

3) 3 cm

12 cm4) 2 cm

3 cm

5)3.5 m

1.5 m

29

4. Pyramid

a) Equilateral Triangular pyramidIt has 4 faces. It has 3 triangular lateral face and one triangularbase.

Example:5 cm

4 cm

4 cmGet the area of the base.

2 cm

BA = h X w2

= 2 cm X 4 cm2

= 8 cm22

= 4 cm2

Get the area of the lateral face.

LA = h X w2 5 cm

= 5 cm X 4 cm2 4 cm

= 20 cm22

= 10 cm2

Get the surface area of the triangular pyramid.

SA triangular pyramid = ( LA X 3 ) + BA= ( 10 cm2 X 3 ) + 4 cm2= 30 cm2 + 4 cm2= 34 cm2

b) Square pyramidIt has 5 faces. It has 4 triangular lateral face and 1 square base.

Example:

2cm

30

6 cm

4 cm

Get the area of the square base.

BA = s2= 4 cm X 4 cm 4 cm= 16 cm2

Get the area of the triangular lateral face.

LA = h X w2

= 6 cm X 4 cm2 6 cm

= 24 cm22

4 cm= 12 cm2

Get the surface area of the square pyramid.

SA square pyramid = (LA X 4 ) + BA= ( 12 cm2 X 4 ) + 16 cm2= 48 cm2 + 16 cm2= 64 cm2

PracticeCompute the surface area of the pyramid.

1)6 m

5 m

2)

3 m

30

6 cm

4 cm


BA = s2= 4 cm X 4 cm 4 cm= 16 cm2


LA = h X w2

= 6 cm X 4 cm2 6 cm

= 24 cm22

4 cm= 12 cm2




1)6 m

5 m

2)

3 m

30

6 cm

4 cm


BA = s2= 4 cm X 4 cm 4 cm= 16 cm2


LA = h X w2

= 6 cm X 4 cm2 6 cm

= 24 cm22

4 cm= 12 cm2




1)6 m

5 m

2)

3 m

30

6 cm

4 cm


BA = s2= 4 cm X 4 cm 4 cm= 16 cm2


LA = h X w2

= 6 cm X 4 cm2 6 cm

= 24 cm22

4 cm= 12 cm2




1)6 m

5 m

2)

3 m

31

21 cm8 m

3)

9 m

5 m

4)

12 m

10 m

5)

16 m7 m

5.ConeTo compute the surface area of a cone, get the area of its base and its

lateral face.

SA cone = LA + BA= + 2

Example:

5 m

5 m

4 m

2 m

32

SA cone = LA + BA= + 2= ( 3.14 ) ( 2 m ) ( 5 m ) + ( 3.14 ) ( 2 m )2= 31.4 m2 + 12.56 m2= 43.96 m2

PracticeFind the surface area of the following cones.

1)8 m

2)9 cm

3)

4)10 cm

5)

16 cm

6.Sphere

3 m

10 cm

15 cm

12 cm

9 cm

32



1)8 m

2)9 cm

3)

4)10 cm

5)

16 cm

6.Sphere

3 m

10 cm

15 cm

12 cm

9 cm

32



1)8 m

2)9 cm

3)

4)10 cm

5)

16 cm

6.Sphere

3 m

10 cm

15 cm

12 cm

9 cm

32



1)8 m

2)9 cm

3)

4)10 cm

5)

16 cm

6.Sphere

3 m

10 cm

15 cm

12 cm

9 cm

33

Below is the formula in getting the surface area of a sphere.

SA sphere =Example:

SA sphere == 4 ( 3.14 ) (2 cm)2= 12.56 X 4 cm2= 50.24 cm2

PracticeFind the surface area of the sphere.

1)

2)

3)

4)

5)

Activity No. 1Compute the surface area of the given spatial figures.

2 cm

9 m

6 m

25 cm

5cm

4 m

33


SA sphere =Example:



1)

2)

3)

4)

5)


2 cm

9 m

6 m

25 cm

5cm

4 m

33


SA sphere =Example:



1)

2)

3)

4)

5)


2 cm

9 m

6 m

25 cm

5cm

4 m

33


SA sphere =Example:



1)

2)

3)

4)

5)


2 cm

9 m

6 m

25 cm

5cm

4 m

34

1) 12 cm

10 10 cm

8 cm

10cm2)

8 cm

15 cm

8 cm

3)

7 cm

8 cm

4)4 cm

15 cm

5)

13 cm

6)

5 cm

2 cm

10 cm

35

Activity No. 2Complete the lateral area, base area and the total surface area of the givenfigures.

Shape Given Parts LA BA SA1.Rectangular

prismL = 3.8 mW 4.2 mH 5.5 m

2.TriangularPyramid

slant height - 8.3 medge of base 5 maltitude of base 4.8 m

3.cylinder Radius 15 cmHeight 22.3 cm

4.cone Radius 14.3 cmSlant height 20.8 cm

5.sphere Radius 120 cm

Lesson No. 3

volumeVolume is the number of cubic units that can exactly be contained in a

three-dimensional or space figure.

Formula in finding the volume of spatial figures:

35



prismL = 3.8 mW 4.2 mH 5.5 m

2.TriangularPyramid





Lesson No. 3




35



prismL = 3.8 mW 4.2 mH 5.5 m

2.TriangularPyramid





Lesson No. 3




35



prismL = 3.8 mW 4.2 mH 5.5 m

2.TriangularPyramid





Lesson No. 3




36

1) Cube = s3

Example: V = s 3= 2 cm X 2 cm X 2 cm= 8 cm3

PracticeFind the volume of the following.

1)

2)

3)

4)

5)2) Rectangular Prism = l X w X h

Example: 15 cm

7

5 cm

V = l X w X h= 15 cm X 5 cm X 7 cm= 525 cm3

2 cm

5 cm

25 cm

12 cm

15 cm

9 cm

7 cm

36

1) Cube = s3



1)

2)

3)

4)


Example: 15 cm

7

5 cm


2 cm

5 cm

25 cm

12 cm

15 cm

9 cm

7 cm

36

1) Cube = s3



1)

2)

3)

4)


Example: 15 cm

7

5 cm


2 cm

5 cm

25 cm

12 cm

15 cm

9 cm

7 cm

36

1) Cube = s3



1)

2)

3)

4)


Example: 15 cm

7

5 cm


2 cm

5 cm

25 cm

12 cm

15 cm

9 cm

7 cm

37


1) 4 m

1.5 m

2) 14 m

6 m

3) 26 cm

9 cm

4) 18 cm

8 cm

5) 6 m

2.5 m

3. Pyramid = l X w X h3

Example:

Height - 4 cm

W 3 cm l 5 cm

V = l X w X h3

= 5 cm X 3 cm X 4 cm

2 m

4 m

12 cm

10 cm

9 m

37


1) 4 m

1.5 m

2) 14 m

6 m

3) 26 cm

9 cm

4) 18 cm

8 cm

5) 6 m

2.5 m


Example:

Height - 4 cm

W 3 cm l 5 cm

V = l X w X h3


2 m

4 m

12 cm

10 cm

9 m

37


1) 4 m

1.5 m

2) 14 m

6 m

3) 26 cm

9 cm

4) 18 cm

8 cm

5) 6 m

2.5 m


Example:

Height - 4 cm

W 3 cm l 5 cm

V = l X w X h3


2 m

4 m

12 cm

10 cm

9 m

37


1) 4 m

1.5 m

2) 14 m

6 m

3) 26 cm

9 cm

4) 18 cm

8 cm

5) 6 m

2.5 m


Example:

Height - 4 cm

W 3 cm l 5 cm

V = l X w X h3


2 m

4 m

12 cm

10 cm

9 m

38

3= 60 cm3

3= 20 cm3


1)

9 cm6 cm

5 cm

2)

24 cm

14 cm10 cm

3)

11 cm

7 cm

6 cm4)

30 cm

15 cm25 cm

5)

38

3= 60 cm3

3= 20 cm3


1)

9 cm6 cm

5 cm

2)

24 cm

14 cm10 cm

3)

11 cm

7 cm

6 cm4)

30 cm

15 cm25 cm

5)

38

3= 60 cm3

3= 20 cm3


1)

9 cm6 cm

5 cm

2)

24 cm

14 cm10 cm

3)

11 cm

7 cm

6 cm4)

30 cm

15 cm25 cm

5)

38

3= 60 cm3

3= 20 cm3


1)

9 cm6 cm

5 cm

2)

24 cm

14 cm10 cm

3)

11 cm

7 cm

6 cm4)

30 cm

15 cm25 cm

5)

39

75 cm

40 cm

60 cm

4.Cylinder - h

Example: 3 m

V = h

= ( 3.14 ) ( 3 m ) 2 ( 5 m)

= ( 3.14 ) ( 9 m2 ) ( 5m )

= ( 28.26 m2 ) ( 5 m )

= 141.3 m3


1) 2.5 m

5 m

6 m

39

75 cm

40 cm

60 cm

4.Cylinder - h

Example: 3 m

V = h

= ( 3.14 ) ( 3 m ) 2 ( 5 m)

= ( 3.14 ) ( 9 m2 ) ( 5m )

= ( 28.26 m2 ) ( 5 m )

= 141.3 m3


1) 2.5 m

5 m

6 m

39

75 cm

40 cm

60 cm

4.Cylinder - h

Example: 3 m

V = h

= ( 3.14 ) ( 3 m ) 2 ( 5 m)

= ( 3.14 ) ( 9 m2 ) ( 5m )

= ( 28.26 m2 ) ( 5 m )

= 141.3 m3


1) 2.5 m

5 m

6 m

39

75 cm

40 cm

60 cm

4.Cylinder - h

Example: 3 m

V = h

= ( 3.14 ) ( 3 m ) 2 ( 5 m)

= ( 3.14 ) ( 9 m2 ) ( 5m )

= ( 28.26 m2 ) ( 5 m )

= 141.3 m3


1) 2.5 m

5 m

6 m

40

2) 4.5 m

5 m3)

15 cm4)

5) 25 cm

5.Cone - h3

Example: r 2 m

h 6 m

50 cm

30 cm

12 m

9 m

41

V = h3

= ( 3.14 ) ( 2 m )2 ( 6 m )3

= (3.14)(4m2)(6m)3

= (12.56 m2) (6m)3

= 75.36 m33

= 25.13 m3

PracticeCompute the volume of the cones.

1)

18 cm

5 cm

2)

55 cm

23 cm

3)

120 cm

4)

65 cm

5 m

41

V = h3

= ( 3.14 ) ( 2 m )2 ( 6 m )3

= (3.14)(4m2)(6m)3

= (12.56 m2) (6m)3

= 75.36 m33

= 25.13 m3


1)

18 cm

5 cm

2)

55 cm

23 cm

3)

120 cm

4)

65 cm

5 m

41

V = h3

= ( 3.14 ) ( 2 m )2 ( 6 m )3

= (3.14)(4m2)(6m)3

= (12.56 m2) (6m)3

= 75.36 m33

= 25.13 m3


1)

18 cm

5 cm

2)

55 cm

23 cm

3)

120 cm

4)

65 cm

5 m

41

V = h3

= ( 3.14 ) ( 2 m )2 ( 6 m )3

= (3.14)(4m2)(6m)3

= (12.56 m2) (6m)3

= 75.36 m33

= 25.13 m3


1)

18 cm

5 cm

2)

55 cm

23 cm

3)

120 cm

4)

65 cm

5 m

42

35 m

5)

50 cm

6.Sphere - 4 3

3

Example:

V = 4 33

= 4 ( 3.14 ) ( 2 m)33

= (12.56) ( 2m X 2m X 2m )3

= ( 12.56 ) ( 8m3 )3

= 100.48 m33

= 33.49 m3

32 cm

r 2 m

43

PracticeCompute the volume of the sphere.

1)

2)

3)

4)

5)

7. Triangular Prism - w X h1 X h22

Example:h2 16 cm

3.5 m

23 cm

12 cm

9 cm

6 cm

43


1)

2)

3)

4)

5)


Example:h2 16 cm

3.5 m

23 cm

12 cm

9 cm

6 cm

43


1)

2)

3)

4)

5)


Example:h2 16 cm

3.5 m

23 cm

12 cm

9 cm

6 cm

43


1)

2)

3)

4)

5)


Example:h2 16 cm

3.5 m

23 cm

12 cm

9 cm

6 cm

44

h1 7 cm

w 9 cm

V = w X h1 X h22

= 9 cm X 7 cm X 16 cm2

= 63 cm2 X 16 cm2

= 31.5 cm2 X 16 cm

= 504 cm3

PracticeCompute the volume of the triangular prism.

11 m1)

9 m

5 m

2) 32 cm

6 cm

10 cm

3) 7.5 m

3 m

4 m

4)

14 cm

9 cm

44

h1 7 cm

w 9 cm

V = w X h1 X h22

= 9 cm X 7 cm X 16 cm2

= 63 cm2 X 16 cm2

= 31.5 cm2 X 16 cm

= 504 cm3


11 m1)

9 m

5 m

2) 32 cm

6 cm

10 cm

3) 7.5 m

3 m

4 m

4)

14 cm

9 cm

44

h1 7 cm

w 9 cm

V = w X h1 X h22

= 9 cm X 7 cm X 16 cm2

= 63 cm2 X 16 cm2

= 31.5 cm2 X 16 cm

= 504 cm3


11 m1)

9 m

5 m

2) 32 cm

6 cm

10 cm

3) 7.5 m

3 m

4 m

4)

14 cm

9 cm

44

h1 7 cm

w 9 cm

V = w X h1 X h22

= 9 cm X 7 cm X 16 cm2

= 63 cm2 X 16 cm2

= 31.5 cm2 X 16 cm

= 504 cm3


11 m1)

9 m

5 m

2) 32 cm

6 cm

10 cm

3) 7.5 m

3 m

4 m

4)

14 cm

9 cm

45

6 cm

5)

20 m

12 m

8 m

Activity No. 1

Compute the volume of the following spatial figures.

1)4 cm

8 cm

2)

8 cm

7 cm

7 cm

3) 4.2 m

10 cm

45

6 cm

5)

20 m

12 m

8 m

Activity No. 1


1)4 cm

8 cm

2)

8 cm

7 cm

7 cm

3) 4.2 m

10 cm

45

6 cm

5)

20 m

12 m

8 m

Activity No. 1


1)4 cm

8 cm

2)

8 cm

7 cm

7 cm

3) 4.2 m

10 cm

45

6 cm

5)

20 m

12 m

8 m

Activity No. 1


1)4 cm

8 cm

2)

8 cm

7 cm

7 cm

3) 4.2 m

10 cm

46

11 m

4)

9 m

5)

5.5 cm

6)18 cm

4 cm

5 cm

7)

8) 9 m4 m

6 m

5 m

25 cm

47

9)

11 cm

7.5 cm5 cm

10)

Activity No. 1Analyze the following problems carefully. Solve them and label your answers.

1) A square portable pool is to be filled with water. If the side of the pool is6.5 m long, how much can it hold ?

2) A swimming pool measures 12 m long by 8 m wide by 5.5 m deep. If filledto the brim, how much water does it hold ?

3) A rectangular flower box measures 50 cm long , 30 cm wide and 45 cmdeep. If this box is to be filled with soil up to 2 cm below the brim. Howmuch soil will it hold ?

2.5 m

47

9)

11 cm

7.5 cm5 cm

10)





2.5 m

47

9)

11 cm

7.5 cm5 cm

10)





2.5 m

47

9)

11 cm

7.5 cm5 cm

10)





2.5 m

48

4) A cylindrical container measures 7.6 cm across the base and is 28.3 cmtall. What is its volume ?

5) A papier-mache ice cream cone for display measures 14.6 dm across thebase and is 27 dm long. What is its volume ?

6) A basketball has a diameter of 30 cm. What is its volume ?

7) A box of cereal is full. If the box is 10 cm long, 9 cm high and 6 cmwide, how many cubic centimeters of cereal are in the box ?

8) The volume of a cylinder is 282.6 cm3 . If it is 10 cm high, what is the areaof the base ?

9) The volume of a triangular prism is 588.75 cm3. If the area of the base is78.5 cm2, what is its height ?

49

10) Determine the volume of a prism whose height is 4.6 cm and whose baseis a trapezoid with bases 6 cm , 8 cm and height of 5 cm.

Chapter 16

49


Chapter 16

49


Chapter 16

49


Chapter 16

50

MeterReading

Lesson No. 1 Electric Meter

Lesson No. 2 Water Meter

Lesson No. 1

Electric ReadingAn electric meter shows the electric power used in kilowatt-hours ( kWh).

It has two kinds, the digital meter and the one with four dials just like the one

shown below, which is the most common in many homes.

50

MeterReading



Lesson No. 1




50

MeterReading



Lesson No. 1




50

MeterReading



Lesson No. 1




51

thousands hundreds tens ones

The ones and the hundreds dials move in clockwise direction, while the

tens and thousands dials move in counter clockwise direction. To know the

electric consumption, just read the number pointed by the dial pointers. What is

the electric reading shown above ?

Electric consumption is measured in kilowatt-hours ( kWh).

To find the electric consumption for a certain period, just subtract the

previous reading from the present reading.

Example:

Previous Reading : 4218 kWh

Present Reading: 4816 kWh

What is the electric consumption ? 4816 - 4218 = 598 kWh

PracticeGive the reading shown in the meters.

__________ 1)

__________2)

__________3)

51









Example:





__________ 1)

__________2)

__________3)

51









Example:





__________ 1)

__________2)

__________3)

51









Example:





__________ 1)

__________2)

__________3)

52

__________4)

__________5)

__________6)

__________7)

__________ 8)

__________9)

__________ 10)

PracticeCompute the electric consumption.

1) Previous Reading

52

__________4)

__________5)

__________6)

__________7)

__________ 8)

__________9)

__________ 10)


1) Previous Reading

52

__________4)

__________5)

__________6)

__________7)

__________ 8)

__________9)

__________ 10)


1) Previous Reading

52

__________4)

__________5)

__________6)

__________7)

__________ 8)

__________9)

__________ 10)


1) Previous Reading

53

Present Reading

Answer: ______________ kWh

2) Previous Reading

Present Reading

Answer: _______________ kWh

3) Previous Reading

Present Reading

Answer: ____________ kWh

4) Previous Reading

54

Present Reading

Answer: ____________ kWh

5) Previous Reading

Present Reading

Answer: ____________ kWh

PracticeCompute the electric consumption of the families and answer the questions thatfollow.

FamilyMeter Reading Electric

ConsumptionPrevious Present1) Reyes 2157 3241 10842) Isidro 8519 9210 6913) Santos 3658 4579 9214) Rodriguez 6728 6819 915) Abad 9152 9843 691

1) Which family has the highest electric consumption ? _________________

54

Present Reading

Answer: ____________ kWh

5) Previous Reading

Present Reading

Answer: ____________ kWh





54

Present Reading

Answer: ____________ kWh

5) Previous Reading

Present Reading

Answer: ____________ kWh





54

Present Reading

Answer: ____________ kWh

5) Previous Reading

Present Reading

Answer: ____________ kWh





55

2) Which family has the least electric consumption ? ___________________

3) Which families have the same electric consumption ? ________________

4) How much more electricity was consumed by Santos family thanRodriguez family ? __________________

5) Who do you think has the most expensive electric bill ? _______________

PracticeRead the solve these problems.

1) The Balagtas family consumed 576 kWh for one month. If the presentreading is 1253, what was the previous reading ?

Mathematical Sentence : _________________________________

Answer: ______________________________________________

2) Last January, the Balagtas family consumed 482 kWh. If their meterreading in December was 876, what was the meter reading in January ?

Mathematical Sentence: _____________________________________

Answer: __________________________________________________

3) What was the average electric consumption of the Balagtas family in a dayif they consumed 482 kWh in the whole month of January ?


Answer: __________________________________________________

4) The Santos family received their electric power consumption notice thatshowed the following :

Present reading - 4568 kWhPrevious reading - 4265 kWh

How many kWh is their electric consumption ?


Answer: __________________________________________________

5) Santos family consumed 211 kWh last October , 189 kWh last Novemberand 203 kWh last December. What is their average electric consumption ?


Answer: __________________________________________________

55








Answer: ______________________________________________



Answer: __________________________________________________



Answer: __________________________________________________





Answer: __________________________________________________



Answer: __________________________________________________

55








Answer: ______________________________________________



Answer: __________________________________________________



Answer: __________________________________________________





Answer: __________________________________________________



Answer: __________________________________________________

55








Answer: ______________________________________________



Answer: __________________________________________________



Answer: __________________________________________________





Answer: __________________________________________________



Answer: __________________________________________________

56

Lesson No. 2

water ReadingWater consumption is measured in cubic meters. The most common type

of water meter that is used in many homes is a digital water meter. This is easier

to read that the use of dials because the water consumed everytime the faucet

turns on registers at once in the meter.

This is how to read a digital water meter.

Cubic meter liter

.56

Lesson No. 2






Cubic meter liter

.56

Lesson No. 2






Cubic meter liter

.56

Lesson No. 2






Cubic meter liter

.

57

A cubic meter is equal to 1000 liters. Suppose these are the numbers

registered in our water meter, how many liters or cubic meters of water was

consumed ?

1) 0003.432 = 3 cubic meters and 432 liters2) 0009.025 = _______________________3) 0029.825 = _______________________4) 0371.209 = _______________________5) 1091.525 = _______________________

To know your water consumption for a certain period of time, subtract the

previous water meter reading from the present reading.

Example:

Present Reading - 368

Previous Reading - 341

Cubic meters consumed 27

PracticeTell how many cubic meters ( m3) and liters of water were consumed in thefollowing meter readings.

1) 0425.003 - _____________________________________

2) 0918.215 - _____________________________________

3) 1254.319 - _____________________________________

4) 4382.421 - _____________________________________

5) 5321.829 - _____________________________________

Practice57

A cubic meter is equal to 1000 liters. Suppose these are the numbers

registered in our water meter, how many liters or cubic meters of water was

consumed ?

1) 0003.432 = 3 cubic meters and 432 liters2) 0009.025 = _______________________3) 0029.825 = _______________________4) 0371.209 = _______________________5) 1091.525 = _______________________

To know your water consumption for a certain period of time, subtract the

previous water meter reading from the present reading.

Example:

Present Reading - 368

Previous Reading - 341

Cubic meters consumed 27

PracticeTell how many cubic meters ( m3) an

Workbook in Matlh Fourth

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