Angles - PBworks

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Angles

Find the measure of angle b.

1)

99°

b

2)

34°

b

3)

243°

31°

b

4)

213°123°

b

5)

74°b

6)

48°

b

7)

60°

b

8)

108°

b

9)

23°b

-1-

Agar

Typewritten Text

Unit 5 - Lesson 1 Worksheet

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10)

94°b

11)

148°b

12)

39°

b

13)

63°b

14)

64°b

15)

57°

b

16) 297°

34°

b

17)

90°

b

18)

221°34°

b

-2-

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19)

137°

b

20)

65°

b

21)

57°b

22)

51°b

23)

81°

b

24)

51°

b

25)

34°

b

26)

42°b

27)

48°

b

28)

39°b

-3-

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29)

107°

b

30)

55°

b

Find the value of x.

31)

38°

(6x + 2)°

32)

91°

(x - 23)°

244°

33)

38°

(x - 45)°

294°34)

52°

(6x + 4)°

35)

56°(6x + 2)°

36)

114°

(5x + 4)°

37)

30°

(4x + 2)°

-4-

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38)

42°

2x°

39)

99°

(32 + x)°

40)

72°6x°

41)

43°(4x + 3)°

42)

123°

3x°

43)

62°

(2x + 4)°

44)

65°

(2x + 5)°

208°

45)

(x - 3)°

2x°

46)

26°

(-41 + x)°

300°

-5-

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47)

133°

(4x + 1)°

48)

38°

(x - 26)°

299°

49)

61°

(3x + 1)°

50)

47°

(2 + 5x)°

-6-

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Angles

Find the measure of angle b.

1)

99°

b

99° 2)

34°

b

34°

3)

243°

31°

b

86° 4)

213°123°

b

24°

5)

74°b

74° 6)

48°

b

48°

7)

60°

b

60° 8)

108°

b

108°

9)

23°b

157°

-1-

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10)

94°b

94° 11)

148°b

32°

12)

39°

b

39° 13)

63°b

27°

14)

64°b

64° 15)

57°

b

33°

16) 297°

34°

b

29° 17)

90°

b

90°

18)

221°34°

b

105°

-2-

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19)

137°

b

137° 20)

65°

b

65°

21)

57°b

57° 22)

51°b

51°

23)

81°

b

81° 24)

51°

b

129°

25)

34°

b

34° 26)

42°b

138°

27)

48°

b

48° 28)

39°b

51°

-3-

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29)

107°

b

107° 30)

55°

b

35°

Find the value of x.

31)

38°

(6x + 2)°

6 32)

91°

(x - 23)°

244°

48

33)

38°

(x - 45)°

294°73 34)

52°

(6x + 4)°

8

35)

56°(6x + 2)°

9 36)

114°

(5x + 4)°

22

37)

30°

(4x + 2)°

7

-4-

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38)

42°

2x°

21 39)

99°

(32 + x)°

49

40)

72°6x°

18 41)

43°(4x + 3)°

10

42)

123°

3x°

41 43)

62°

(2x + 4)°

12

44)

65°

(2x + 5)°

208°

41 45)

(x - 3)°

2x°

31

46)

26°

(-41 + x)°

300°75

-5-

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47)

133°

(4x + 1)°

33 48)

38°

(x - 26)°

299°

49

49)

61°

(3x + 1)°

20 50)

47°

(2 + 5x)°

9

-6-

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5.3

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.

1)

x

9.2 m

11.1 m

2) 4.8 yd

9.9 yd

x

3)

10.4 ft

7.9 ft

x

4)

x

4.9 m

12.5 m

5)

6.1 cm 9.8 cm

x

6)

11.2 cm

x

11.7 cm

7) 4 ft

4 ft

x

8) 9.6 in

x

12.2 in

9)

11.1 in

x

15.2 in

10)

x

5.2 cm

15.2 cm

Agar

Typewritten Text

Unit 5 - Lesson 3 Worksheet

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Answers to 5.3

1) 6.2 m 2) 11 yd 3) 13.1 ft 4) 11.5 m

5) 11.5 cm 6) 3.4 cm 7) 5.7 ft 8) 7.5 in

9) 10.4 in 10) 14.3 cm

Unit 5 – Lesson 4 Worksheet

Medians of Triangles Find the centroid of the following triangles.

Find the orthocentre of the following triangles.

Unit 5 – Lesson 4 WorksheetB

Word Problems with 3D shapes Name: _________________

1. For the formula rC 2 solve for r.

2. For the formula rhrA 22 2 solve for h.

3. For the formula hrV 2 solve for: A. r B. h

4. For the formula 24 rA solve for r.

5. For the formula 3

4 3rV

solve for r.

6. For the formula rsrA 2 solve for s.

7. For the formula hrV 2

31 solve for:

A. r B. h

8. For the formula 2

21 bbsA solve for s.

9. For the formula hbV 2

31 solve for:

A. b B. h

10. The width and length of a rectangular box is 12 cm and 8 cm respectively. Determine the height of the box if it has a surface area of 2100 cm2.

11. Determine the volume of a snowball that has a surface area of 3300 cm2.

12. The volume of a cone is 100 m3. If the radius is 1.5 m, determine the surface area.

13. Answer the following:

1. The volume of a rectangular prism is 64a

3b

6. If the area of the base is

16ab3, which expression represents

the height of the prism? A. 4a

2b

3

B. 4a3b

3

C. 1024a3b

9

D. 1024a4b

9

2. A rectangular field has a perimeter of (10a – 6) metres and a width of 2a metres. Which expression represents the length of the field? A. 8a – 6 B. 12a – 6 C. 3a – 3 D. 3a

2 - 3

3. A circular table is covered with a square cloth with a side length equal to the diameter of the table. Approximately what percentage of the tablecloth hangs down from the table?

A. 17.5% B. 19% C. 21.5% D. 25%

4. A hat in the shape of a cone is made from a sheet of stiff paper. If the cone has a base diameter of 16 cm and a slant length of 30 cm, how much material was used to make the hat?

A. 216 cm

B. 260 cm

C. 2240 cm

D. 2480 cm

5. A pot for boiling water is 25 cm in diameter and 10 cm high. About how many litres of water does the pot hold when filled to a height of 8 cm? (One litre of water holds 1000 cm3)

A. 3 L B. 3.5 L C. 4 L D. 4.5 L

6. Three cylindrical cans are used for the storage of food. They are related as follows:

Can B has twice the height of Can A but has the same radius.

Can C has twice the radius of Can A but has the same height. What is the ratio, A:B:C, of the volumes of the cans?

A. 1:2:2 B. 1:2:4 C. 1:4:2 D. 1:4:8

7. The ratio of the volume of a cube with

side length 2 cm to a cylinder with diameter 2 cm and height 2 cm would be:

A. 2:1

B. 3:

C. 4:

D. 4:3

14. An ice cream container is cylindrical with diameter 30 cm and height 50 cm and

is filled with ice cream. The ice cream scoop makes ice cream scoops of diameter 6 cm. How many one-scoop cones can be made from one container of ice cream?

15. Spherical balloons are filled with helium gas at a rate where the surface area is

increasing at 25 cm2/s. What will the radius of a balloon that has been filled for 4 s?

16. A 20 cm pencil is in the shape of a cylinder. When the pencil is sharpened, the

tip is a cone with a height of 4 cm. Since the volume of a cone is one-third that of a cylinder with the same height and radius, Emily has calculated that about 13% of the volume of the pencil was removed in the sharpening. Was his calculation reasonable? Show your work.

17. Every spring Joanna orders a load of soil to add to her gardens. This year,

Joanna paid for a truckload of soil that was supposed to be 3 m3. A. The soil formed a conical pile with a diameter of 3 m and height 1.5 m.

Did she receive the amount of soil promised? Show your work. B. She wanted to bring the soil to her backyard using a wheelbarrow. She

approximated a wheelbarrow load to be a rectangular prism with dimensions 50 cm by 40 cm by 35 cm. How many trips would she have to make with the wheelbarrow to transport all the soil to her backyard?

C. Joanna will be adding the dirt to three gardens. One garden is a rectangle 5 m by 12 m, the second garden is a triangle with base 4 m and height 3 m and the third garden is a circle with diameter 4 m. What is the height of soil she will be able to add to the three gardens if she plans to spread it evenly?

Subject: Math

Unit: Surface Area and Volume Lesson: Three

email:[email protected] www.youtheducationservices.ca

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Comparing Volume to Surface Area in 3D Objects Worksheet

1. A toy company is planning to market a new doll. The doll will need a box

that has a volume of 125 cm³. Design a box with the smallest possible surface area.

2. Now design a box with a larger surface area but still the same volume.

3. A breakfast cereal company is having a competition to have someone

design a new box for their latest creation. The only requirement is that the box has a volume of 64 cm³. Design two boxes that fit the criteria.

4. Find the volume of a prism with the dimensions 90 cm by 50 cm by

30 cm high.

5. If the volume for a rectangular prism can be found with the formula V = (30 cm²) × 55 cm, what would the surface area of this prism be?

6. Find the surface area and volume of the building shown below.

1 -

90 cm 50 cm

30 cm

14 m

60 m 25 m

Subject: Math




-

7. Find the volume of a prism with the S.A. = 4(3 cm × 4 cm) + 2(4 cm × 4 cm).

8. Redesign the prism shown below so it has the same

volume, yet a smaller surface area. Prism has length of 128 cm by 2 cm wide by 2 cm high. V =

512 cm³

9. Find the surface area of the set of building blocks shown.

2 -

2 cm 2 cm

128 cm

2 cm 5 cm 3 cm

3 cm

3 cm

4 cm

4 cm

7 cm

3 cm

Subject: Math




-

10. A local architect is planning to build two buildings on the same development. Each building will have the same volume, 2500m³, but she wants two unique structures when she is done. Can you help her plan her two buildings?

3 -

Subject: Math




- 4 -

Comparing Volume to Surface Area in 3D Objects Worksheet Solutions

1. A toy company is planning to market a new doll. The doll will need a box

that has a volume of 125 cm³. Design a box with the smallest possible surface area.

ANSWER V = Area × h V = l × w × h V = 5 cm × 5 cm × 5 cm V = 125 cm³ S.A. = 6(Area of square) S.A. = 6(5 cm × 5 cm) S.A. = 150 cm²

2. Now design a box with a larger surface area but still the same volume.

ANSWER (there are more than one option) S.A. = 2(Area of Rectangle A) + 2(Area of Rectangle B) + 2(Area of Rectangle C) S.A. = 2(62.5 cm × 1 cm) + 2(62.5 cm × 2 cm) + 2(2 cm × 1cm) S.A. = 125 cm² + 250 cm² + 4 cm² S.A. = 379 cm²

3. A breakfast cereal company is having a competition to have someone

design a new box for their latest creation. The only requirement is that the box has a volume of 64 cm³. Design two boxes that fit the criteria.

Subject: Math




-

ANSWERS (there are numerous other options) A. S.A. = 6(Area of square) S.A. = 6(4 cm × 4 cm) S.A. = 96 cm² B. S.A. = 2(Area of Rectangle A) + 2(Area of Rectangle B) + 2(Area of Rectangle C) S.A. = 2(32 cm × 1 cm) + 2(32 cm × 2 cm) + 2(2 cm × 1 cm) S.A. = 64 cm² + 128 cm² +4 cm² S.A. = 196 cm²

4. Find the volume of a prism with the dimensions 90 cm by 50 cm by

30 cm high.

ANSWER V = Area × h V = l × w × h V = (90 cm × 50 cm) × 30 cm V = 135 000 cm³

5 -

90 cm 50 cm

30 cm

Subject: Math




-

5. If the volume for a rectangular prism can be found with the formula V = (30 cm²) × 55 cm, what would the surface area of this prism be?

ANSWER S.A. = 2(Area of square) + 4(Area of rectangle) S.A. = 2(30 cm × 30 cm) + 4(30 cm × 55 cm) S.A. = 1800 cm² + 3300 cm² S.A. = 5100 cm²

6. Find the surface area and volume of the building shown below.

ANSWER V = l × w × h V = (60 m × 25 m) × 14 m V = 21 000 m³ S.A. = 1(Area of Rectangle A) + 2(Area of Rectangle B) + 2(Area of Rectangle C) S.A. = 1(60 m × 25 m) + 2(60 m × 14 m) +2(25 m × 14 m) S.A. = 1500 m² + 1680 m² + 700 m² S.A. = 3880 m² Remember that you would not include the floor as a part of the total surface area of the building.

6 -

14 m

60 m 25 m

Subject: Math




-

7. Find the volume of a prism with the S.A. = 4(3 cm × 4 cm) + 2(4 cm × 4 cm).

ANSWER V = Area × h V = l × w × h V = (4 cm × 3 cm) × 4 cm V = 48 cm³

8. Redesign the prism shown below so it has the same volume, yet a

smaller surface area. Prism has length of 128 cm by 2 cm wide by 2 cm high. V = 512 cm³

ANSWER A cube with a volume of 512 cm³ S.A. = 6 (area of square) S.A. = 6(8 cm × 8 cm) S.A. = 384 cm²

7 -

2 cm 2 cm

128 cm

Subject: Math




-

9. Find the surface area of the set of building blocks shown. ANSWERS A S.A. = 2(Area of Rectangle A) + 2(Area of Rectangle B) + 2(Area of Rectangle C) S.A. = 2(2 cm × 5 cm) + 2(2 cm × 3 cm) + 2(5 cm × 3 cm) S.A. = 10 cm² + 12 cm² + 30 cm² = 52 cm² B S.A. = 2(Area of square) + 4(Area of rectangle) S.A. = 2(4 cm × 4 cm) + 4(4 cm × 7 cm) S.A. = 16 cm² + 54 cm² = 70 cm² C S.A. = 6(Area of square) S.A. = 6(3 cm × 3 cm) S.A. = 54 cm²

8 -

2 cm 5 cm 3 cm

3 cm

3 cm

4 cm

4 cm

7 cm

3 cm

Subject: Math




-

10. A local architect is planning to build two buildings on the same development. Each building will have the same volume, 2500m³, but she wants two unique structures when she is done. Can you help her plan her two buildings?

ANSWERS (many possibilities) A. 10 m by 5 m by 50 m high B. 10 m by 10 m by 25 m high

9 -

Angles - PBworks

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