M1A Warm Up:Just try this and see if you can remember…

The distance from Raleigh to Wilmington is 120 miles, the distance from Wilmington to Charlotte is 200 miles, and the distance from Raleigh to Charlotte is 160 miles. Do the three towns form a right triangle? Explain.

Yes; The Pythagorean Theorem is true for these three values. 1602 + 1202 = 2002

Homework Check:Document Camera

Objective:Students will be able to:

•Use formulas for rectangles, triangles, circles, cylinders, cones.•To solve literal equations

Area Formulas

Rectangle

Rectangle

What is the area formula?

Rectangle

What is the area formula? bh

Practice!Rectangle

Square

10m

17m

14cm

AnswersRectangle

Square

10m

17m

14cm

196 cm2

170 m2

So then what happens if we cut a rectangle in half?

What shape is made?

TriangleSo then what happens if we

cut a rectangle in half? What shape is made?

TriangleSo then what happens if we

cut a rectangle in half? What shape is made?

2 Triangles

TriangleSo then what happens if we

cut a rectangle in half? What shape is made?

2 Triangles

So then what happens to the formula?

TriangleSo then what happens if we

cut a rectangle in half? What shape is made?

2 Triangles

So then what happens to the formula?

TriangleSo then what happens if we

cut a rectangle in half? What shape is made?

2 Triangles

So then what happens to the formula?

bh

TriangleSo then what happens if we

cut a rectangle in half? What shape is made?

2 Triangles

So then what happens to the formula?

bh2

Practice!Triangle

5 ft

14 ft

Answers35 ft2Triangle

5 ft

14 ft

A prism is a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms. A cylinder has two circular bases.

Area of a Circle

The Area (A) of a Circle is found by solving the following formula:

7 cm

Find the area of the circle.

A = π r

2

1. Substitute the radius into formula.

A = π (7)2

2. Use 3.14 as an approximation for π.A = 3.14(49)

A = 153.86 cm2

3. Don't forget to label the units as square units.

What is the Area (A) of a Circle with a radius (r) of 8 m?

8 m

What is the Area (A) of the circle?

What is the Area (A) of the circle?

VOLUME OF PRISMS AND CYLINDERSWords Numbers Formula

Prism: The volume V of a prism is the area of the base B times the height h.

Cylinder: The volume of a cylinder is the area of the base B times the height h.

B = 2(5)= 10 units2

V = 10(3)

= 30 units3

B = p(22)= 4p units2

V = (4p)(6) = 24p 75.4 units3

V = Bh

V = Bh

= (pr2)h

Show Brainpop video on Cylinders.

Ex 1: Find the volume of each figure to the nearest tenth.

A rectangular prism with base 2 cm by 5 cm and height 3 cm.

= 30 cm3

B = 2 • 5 = 10 cm2

V = Bh

= 10 • 3

Area of base

Volume of a prism

Ex 2: Find the volume of the figure to the nearest tenth.

4 in.

12 in.

= 192 p 602.88 in3

B = p(42) = 16p in2

V = Bh

= 16p • 12

Area of base

Volume of a cylinder

A pyramid is named for the shape of its base. The base is a polygon, and all of the other faces are triangles. A cone has a circular base. The height of a pyramid or cone is measured from the highest point to the base along a perpendicular line.

VOLUME OF PYRAMIDS AND CONES

(22)

13V = • 9 • 10

V = 30 94.2 in3

V = Bh13

B = (32) = 9 in2

Use 3.14 for .

Ex 7: Find the volume of the figure.

Solving Formulas WSComplete the front with Mrs. Childrey

Literal EquationsThis means to solve an equation for one

variable in terms of another variable.

1) Solve 2x - 4y = 7 for xTo get x by itself, what is the first step?

1. Add 2x2. Subtract 2x3. Add 4y4. Subtract 4y

Answer Now

L1) Solve 2x - 4y = 7 for x

L1) Solve 2x - 4y = 7 for x1. Draw “the river”2. Add 4y to both

sides3. Simplify4. Divide both sides

by 25. Does it simplify?

+ 4y + 4y

2x = 7 + 4y

2 27 4

2

yx

x = 2y + 3.5

L2) Solve 2x - 4y = 7 for yTo get y by itself, what is the first step?

1. Add 2x2. Subtract 2x3. Add 4y4. Subtract 4y

Answer Now

L2) Solve 2x - 4y = 7 for y1. Draw “the river”

2. Subtract 2x from both sides

3. Simplify

4. Divide both sides by -4

5. Does it simplify?

- 2x - 2x

-4y = 7 - 2x

-4 -47 2

4

xy

y = 0.5x - 1.75

L3) Solve for y.

What is the first step?

y a3

c

1. Multiply by 32. Divide by 33. Add a4. Subtract a

Answer Now

L3) Solve for y:y a

3c

1. Draw “the river”

2. Clear the fraction – multiply both sides by 3

3. Simplify

4. Subtract a from both sides

5. Simplify

y + a = 3c

-a -a

y = 3c - a

3 33

y ac

L4) Solve for y: 4x – 2y = 121. -4x + 122. 4x - 123. -2x + 64. 2x - 6

Answer Now

L4) Solve for y: 4x – 2y = 12

1. Draw “the river”

2. Subtract 4x from both sides

3. Simplify

4. Divide both sides by -2

5. Does it simplify?

- 4x - 4x

-2y = 12 – 4x

-2 -2

y = -6 + 2x

or y = 2x - 6Yes!

1. L = V - WH

2.

3.

4.

L5) The formula for the volume of a rectangular prism is V = LWH. Which equation solves the formula for L?

LV H

W

LVW

H

LV

HW Answer Now

1. h = 3Vb

2.

3.

4.

L6) The formula for the volume of a pyramid is V = . Which equation solves the formula for h?

Answer Now

1

3bh

h 3b

V

h 3V

b

h V

3b

Classwork: Literal equations part 1 #1-12

Homework:Literal Equations #11 and 12

And Back of Solving Formulas WS