match each term to its corresponding definition. · 2011-11-07 · 5. 6. calculate the surface area...

Chapter 12 l Skills Practice 905

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Skills Practice Skills Practice for Lesson 12.1

Name _____________________________________________ Date ____________________

Box It Up Nets and Platonic Solids

VocabularyMatch each term to its corresponding definition.

1. base of polyhedron a. a three-dimensional solid formed by polygons

that enclose a region 2. edge of polyhedron

b. one of the polygons forming a polyhedron 3. face of polyhedron

c. a face on top or bottom of a polyhedron 4. lateral edge of polyhedron

d. any face of a polyhedron that is not a base 5. lateral face of polyhedron

e. a segment formed by the intersection of two

faces on a polyhedron 6. net

f. an edge formed by the intersection of two

lateral faces on a polyhedron

7. polyhedron

g. the point of intersection of three or more

faces on a polyhedron

8. regular polyhedron

h. a three-dimensional solid formed by regular

polygons

9. vertex of polyhedron

i. a two-dimensional representation

of a polyhedron

906 Chapter 12 ● Skills Practice

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Problem Set

Identify the base(s) of each polyhedron. Then classify the polyhedron that would be formed by each net.

1.

Base

2.

The polyhedron is apentagonal pyramid.

3. 4.

Chapter 12 ● Skills Practice 907

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5. 6.

Calculate the surface area of each polyhedron given its net. Each grid

square represents a square that is 1 __ 2 centimeter long and 1 __

2 centimeter wide.

Use 3.14 for � and round to the nearest hundredth, if necessary.

7. 8.

SA � Area of base � 4 � Area of triangular faces

SA � (3)(3) � 4 ( 1 __ 2

) 3 � 4

SA � 9 � 4(6)

SA � 9 � 24

SA � 33 cm2


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9. 10.

11. 12.


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Label the visible bases and lateral faces of each prism.

13. Base

LateralFace

14.

15. 16.

17. 18.

Determine the number of faces, edges, and vertices for each polyhedron.

19. 20.

There are 7 faces, 12 edges, and7 vertices.


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21. 22.

23. 24.

25. 26.


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27. 28.

Describe the polygons used to create each polyhedron.

29. 30.

2 trapezoids, 4 rectangles

31. 32.


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33. 34.

35. 36.

Draw a net for each polyhedron based on its description. Each grid square represents a square that is 1 __

2 centimeter long and 1 __

2 centimeter wide.

37. A triangular prism has a height of 3 centimeters, a width of 2 centimeters, and

a length of 4 centimeters.


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38. A cube has a side length of 3 centimeters.

39. A square pyramid has a width of 4 centimeters and a height of 3 centimeters.

40. A cylinder has a height of 4 centimeters and a diameter of 1 centimeter.


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41. A rectangular prism has a height of 1 centimeter, a width of 2 centimeters, and a

length of 5 centimeters.

42. A rectangular pyramid has a height of 2 centimeters, and a base with a length of

6 centimeters and a width of 4 centimeters.


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Name _____________________________________________ Date ____________________

Backyard Barbeque Introduction to Volume and Surface Area

VocabularyAnswer each question.

1. Suppose that you measured the amount of rice that would fit into a cube.

What does the amount of rice in the cube represent? Explain your answer.

2. Use a real life example to describe surface area.

Problem SetCalculate the volume of each rectangular prism.

1.

8 in.

5 in.

2 in.

2.

1.5 cm3 cm

14 cm

V � (8) � (2) � (5)

V � 80 in.3

3.

8 m

3.5 m2 m

4.

8 m

13 m5 m


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5.

4 in.

4 in.4 in.

6.

21 ft6 ft

9 ft

Describe how you would separate each solid to calculate its volume.

7.

Separate the solid into two rectangular prisms – one prism is the bottom of the “L”, and the other prism is the top of the “L”.

8.

9.


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10.

11.

12.


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Calculate the volume of each solid formed by rectangular prisms.

13.

2 ft

1 ft

1 ft

3 ft

1 ft

14.

5 m

1 m

6 m

4 m

1 m

V � top prism � bottom prism

V � (1)(1)(1) � (4)(1)(1)

V � 1 � 4

V � 5 ft3

15. 2 cm 2 cm

1 cm

2 cm

2 cm

2 cm

6 cm

1 cm

6 cm

16.

6 yd

4 yd

1 yd

2 yd2 yd

2 yd


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17.

12 ft

2 ft

1 ft9 ft

1 ft 2 ft 18. 1 mm 1 mm

19 mm

15 mm1 mm

12 mm

Calculate the surface area of each rectangular prism.

19.

2 m

8 m

3 m

20.

1.5 in.9 in.

3 in.

SA � front � back � side � side � top � bottom

SA � 24 � 24 � 16 � 16 � 6 � 6

SA � 92 m2


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21.

4 cm

6 cm

11 cm

22.

23 m

12 m

5 m

23.

10 mm3 mm

9 mm

24.

12 yd

12 yd

3 yd

Determine the number of outside surfaces that each solid has. Then describe the surfaces.

25.

There are 8 outside surfaces. Six are lateral faces in the shape of rectangles. Two are the bases that have an L shape.


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26.

27.

28.

29.


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30.


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Turn Up the Volume and Let’s Bend Light Beams Volume and Surface Area of a Prism

VocabularyWrite the term from the box that best completes each statement.

bases of a prism lateral faces of a prism right prism

height of a prism oblique prism surface area of a prism

lateral edges of a prism prism volume of a prism

1. A(n) is a polyhedron formed by parallelograms.

The corresponding sides of two congruent and parallel polygons are connected.

2. The are the two congruent and parallel faces

on a prism.

3. The are the parallelograms connecting the

corresponding sides of the bases on a prism.

4. The are formed by the intersection of the lateral faces

on a prism.

5. The is the perpendicular distance between the two

bases of a prism.

6. A(n) is a prism with rectangular faces.

7. A(n) is a prism with parallelogram faces.

8. The is the amount of space inside a prism.

9. The is the total outside area of a prism.


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Problem SetUse your pencil to make bold one base of each prism.

1. 2.

3. 4.

5. 6.

Classify each polyhedron and state whether it is oblique or right.

7. 8.

oblique parallelogram prism


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9. 10.

11. 12.

Calculate the volume of each right prism.

13.

7 m

7 m7 m

14. 1.5 cm

2.5 cm

6 cm

V � Bh

V � 73

V � 343 m3

15.

4 ft

2 ft

10 ft

16.

4 ft

2 ft8 ft


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17.

3.5 cm

3.5 cm

3.5 cm

18. 9 yd

3 yd

2 yd

6.2 yd

Calculate the surface area of each right prism.

19. 2.4 m

6 m

3 m

20.

5.5 ft

5.5 ft5.5 ft

SA � 2lw � 2wh � 2lh

SA � 2(2.4)(3) � 2(3)(6) � 2(2.4)(6)

SA � 4.8(3) � 6(6) � 4.8(6)

SA � 14.4 � 36 � 28.8

SA � 79.2 m 2

21. 5 in.

3 in.

2 in.4 in.

22. 2 m

5 m

5 m

7 m


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23. 12 yd

7 yd 5 yd

1.5 yd 24.

5 ft

8 ft

5 ft

16 ft

14 ft

4 ft

Each table shows possible dimensions of a rectangular prism with a given volume. Complete each table to determine the rectangular prism with the smallest surface area and the given volume.

25. 27 ft3

Length(ft)

Width(ft)

Height(ft)

Volume(cu ft)

Surface Area(sq ft)

1 1 27 1(1)(27) � 27 2(1)(1) � 2(1)(27) � 2(27)(1) � 110

1 3 9 1(3)(9) � 27 2(1)(3) � 2(3)(9) � 2(9)(1) � 78

1 9 3 1(9)(3) � 27 2(1)(9) � 2(9)(3) � 2(3)(1) � 78

3 3 3 3(3)(3) � 27 6(3)(3) � 54

9 3 1 9(3)(1) � 27 2(9)(3) � 2(3)(1) � 2(1)(9) � 78

27 1 1 27(1)(1) � 27 2(27)(1) � 2(1)(1) � 2(1)(27) � 110

The smallest surface area is 54 square feet. The prism that has this surface area has a length of 3 feet, a width of 3 feet, and a height of 3 feet.


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26. 8 m3

Length(m)

Width(m)

Height(m)

Volume(cu m)

Surface Area(sq m)

1 1 8

1 2 4

1 4 2

2 2 2

2 4 1

8 1 1

27. 60 cm3

Length(cm)

Width(cm)

Height(cm)

Volume(cu cm)

Surface Area(sq cm)

2 2 15

2 3 10

2 6 5

10 3 2

3 10 2

15 2 2


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28. 120 yd3

Length (yd)

Width (yd)

Height (yd)

Volume (cu yd)

Surface Area (sq yd)

2 6 10

3 5 8

2 3 20

2 12 5

8 3 5

2 5 12

29. 36 m2

Length (m)

Width (m)

Height (m)

Volume (cu m)

Surface Area (sq m)

1 6 6

1 3 12

1 4 9

2 3 6

2 2 9

3 3 4


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30. 24 ft2

Length (ft)

Width (ft)

Height (ft)

Volume (cu ft)

Surface Area (sq ft)

1 1 24

1 3 8

1 4 6

1 2 12

2 2 6

2 4 3


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Name _____________________________________________ Date ____________________

Modern-Day Pyramids and Soundproofing Volume and Surface Area of a Pyramid

VocabularyDraw a diagram to illustrate each term.

1. pyramid 2. base of a pyramid

3. lateral face of a pyramid 4. lateral edge of a pyramid

5. vertex of a pyramid 6. height of a pyramid

7. regular pyramid 8. slant height of a pyramid


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Define each term in your own words.

9. volume of a pyramid

10. surface area of a pyramid

11. lateral area of a pyramid

12. composite solid

Problem Set Classify each polyhedron as completely as possible.

1. 2.

Rectangular prism

3. 4.

5. 6.


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7. 8.

Calculate the volume of each pyramid.

9. 5 m

3 m

3 m

10. 6 ft

3 ft

10 ft

V � 1 __ 3 Bh

V � 1 __ 3 (3)(3)(5)

V � 15 m 3

11.

6 in.4 in.

10 in.

12. 12 m

6 m

4 m


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13. 4 cm

3 cm

2 cm

14.

4 ft

6 ft

3 ft

3 ft

15.

8 ft

6 ft5 ft

16.

7 m

5 m

6 m

4 m

Calculate the lateral area of each pyramid.

17. 3 in.

4 in.

4 in.

18.

5 m

7 m

A � (4) � 1 __ 2 (4)(3)

A � 24 in.2


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19.

7 in.

6 in.

6 in.

20. 4 m

9 m

21.

6 yd

8 yd

22. 5 m

7 m

Calculate the surface area of each pyramid. Round to the nearest tenth.

23. 7 in.

12 in.

12 in.

24. 6 m

5.5 m

5.5 m

SA � B � 1 __ 2 Pl

SA � (12)(12) � 1 __ 2 (48)(7)

SA � 144 � 168

SA � 312 in.2


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25.

4 cm

4 cm

4 cm

4 cm

3.5 cm

26. 2 ft

7.5 ft

7.5 ft

27. 9 cm

3 cm3 cm

28. 7 yd

8 yd8 yd

Calculate the total surface area of each composite solid.

29.

5 ft

8 ft

2 ft

4 ft

3 ft

Total SA � 2(5 ) 2 � 2(2 � 8) � 4(5) � 3(4) � 8(4) � 2(4 � 5) � 2(4 � 2)

� 202 f t 2


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30. 6 in.

4.5 in.

5 in.

3 in.

3 in. 8 in.

31.

5 ft

6 ft

6 ft6 ft

5.8 ft

32. 6.5 m 7 m

3 m

10 m5 m


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33.

5 ft

5 ft

5 ft

6.5 ft6 ft

8 ft5 ft

2 ft

34. 8 in.

8 in.

8 in.8 in.

12 in.6 in.


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Making Concrete Stronger Volume and Surface Area of a Cylinder

VocabularyExplain how each set of terms are related.

1. cylinder, bases of a cylinder, and radius of a cylinder

2. axis of a cylinder and height of a cylinder

3. right cylinder and oblique cylinder

4. volume of a cylinder and surface area of a cylinder

Problem Set

Identify the radius, diameter, and height of each cylinder.

1. 8 cm

10 cm

2. 7 m

15 m

Radius: 4 cm

Diameter: 8 cm

Height: 10 cm


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3. 12 ft

12 ft

4. 20 in.

9 in.

5. 7 mm

8 m

m

6. 4 yd

12 yd

Use your knowledge of measurement conversions to answer each question.

7. A cylinder has a height of 50 inches and a diameter of 2 feet. What is the diameter

of the cylinder in inches?

2 feet � 12 inches __________ 1 foot

� 24 inches

8. A cylinder has a height of 5 centimeters and a diameter of 16 millimeters. What is

the height of the cylinder in millimeters?

9. A cylinder has a height of 3 yards and a diameter of 7 feet. What is the height of

the cylinder in feet?


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10. A cylinder has a height of 600 centimeters and a diameter of 1.5 meters. What is

the diameter of the cylinder in centimeters?

11. A cylinder has a height of 0.7 foot and a diameter of 7 inches. What is the height of

the cylinder in inches?

12. A cylinder has a height of 7000 millimeters and a diameter of 2 meters. What is the

height of the cylinder in meters?

Calculate the volume of each cylinder. Use 3.14 for �. Round decimals to the nearest tenth, if necessary.

13. 5.5 m

7 m

14. 30 yd

22 yd

V � �r 2h

V � �(5.5)2(7)

V � 211.75�

V � 664.9 m3

15. 20 m

5 m

16. 10 ft

4.5 ft


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17. 4 mm

6 mm

18. 16 ft

5 ft

19. 9 m

12 m

20. 3.5 cm

13 cm

Suppose that each cylinder is unfolded to form a net. Calculate the area of the rectangle in each net. Use 3.14 for �. Round decimals to the nearest tenth, if necessary.

21. 7 in.

7 in.

22.

8 m

6 m

A � 2(3.14)(7)(7)

A � 307.7 in2


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23.

6 ft

2 ft 24. 3.2 in.

5 in.

25.

3 m

2.1 m

26. 7 yd

10 yd

Calculate the surface area of each cylinder. Use 3.14 for �. Round decimals to the nearest tenth, if necessary.

27. 7 in.

7 in.

28. 6 m

8 m

SA � 2�rh � 2�r 2

SA � 2�(7)(7) � 2�(7)2

SA � 196�

SA � 615.4 in.2


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29.

6 ft

2 ft 30. 3.2 in.

5 in.

31. 4 cm

7.4 cm

32. 10 ft

4 ft


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33. 5 ft

7.5 ft

34. 15 yd

32 yd


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Sand Piles Volume and Surface Area of a Cone

VocabularyIdentify and label each term in the diagram of the cones.

1. base

2. radius

3. axis

4. altitude

5. height

6. slant height

Write the term that best completes each sentence.

7. The cone on the left can be described as a(n) cone.

8. The cone on the right can be described as a(n) cone.

9. The of a cone is the amount of space inside of the cone.

10. The of a cone is the amount of outside surface of the cone.


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Problem SetCalculate the volume of each cone. Use 3.14 for �. Round decimals to the nearest tenth, if necessary.

1. h = 6 mm

r = 5 mm

2. 12 m

20 m

V � 1 __ 3 �r

2h

V � 1 __ 3 �(5)2(6)

V � 50�

V � 157 mm3

3.

7 ft

10 ft 4.

4 yd

11 yd


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5. 6 m

[ 8 m ]

6.

3 ft

[ 3 ft ]

7. 8 in.

3 in.

8. 2 mm

5 mm

Use the given dimensions of each cone to calculate the lateral area. Use 3.14 for �. Round decimals to the nearest tenth, if necessary.

9. The radius of the base is 2 inches. The slant height is 10.1 inches.

LA � �r l

LA � 3.14(2)(10.1)

LA � 63.4 in.2


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10. The radius of the base is 6 feet. The slant height is 7.2 feet.

11. The radius of the base is 2.3 meters. The slant height is 8.1 meters.

12. The radius of the base is 3.8 centimeters. The slant height is 4 centimeters.

13. The diameter of the base is 6 yards. The slant height is 2 yards.

14. The diameter of the base is 5 millimeters. The slant height is 2.9 millimeters.

15. The diameter of the base is 4.2 inches. The slant height is 4.4 inches.

16. The diameter of the base is 7.2 feet. The slant height is 7.2 feet.


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Calculate the surface area of each cone. Use 3.14 for �. Round decimals to the nearest tenth, if necessary.

17. 9 in.

5 in.

18. 14 m

12 m

SA � �r 2 � �r l

SA � �(5)2 � �(5)(9)

SA � 25� � 45�

SA � 70�

SA � 219.8 in.2

19. 4 in.

3 in.

2.5 in. 20. 15 ft

16 ft

21. 4.12 in. 4 in. 1 in.

22.

5 ft 4 ft

3 ft


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23. 13 m

5 m

24. 7 yd

21 yd22.1 yd

Use the given information to answer each question.

25. Cone A has a radius of 7 inches and a height of 9 inches. Cone B has a radius of

3 inches and a height of 12 inches. How do their volumes compare? Explain.

Cone A: Cone B:

V � 1 __ 3 �r 2h V � 1 __

3 �r 2h

V � 1 __ 3 �(7)2(9) V � 1 __

3 �(3)2(12)

V � 147� in.3 V � 36� in.3

Cone A has a much greater volume than cone B.

26. Cone A has a radius of 5 feet and a height of 15 feet. Cone B has a radius of

15 feet and a height of 5 feet. How do their volumes compare? Explain.


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27. Cone A has a diameter of 10 yards and a height of 2 yards. Cone B has a radius of

6 yards and a height of 9 yards. How do their volumes compare? Explain.

28. Cone A has a diameter of 9 centimeters and a height of 19 centimeters. Cone B

has a radius of 16 centimeters and a height of 6 centimeters. How do their volumes

compare? Explain.

29. Cone A has a radius of 13 millimeters and a slant height of 7 millimeters. Cone B

has a radius of 9 millimeters and a slant height of 11 millimeters. How do their

surface areas compare?


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30. Cone A has a radius of 20 feet and a slant height of 10 feet. Cone B has a radius of

10 feet and a slant height of 20 feet. How do their surface areas compare?

31. Cone A has a diameter of 13 millimeters and a slant height of 12 millimeters.

Cone B has a diameter of 15 millimeters and a slant height of 10 millimeters.

How do their surface areas compare?

32. Cone A has a diameter of 7 inches and a slant height of 7 inches. Cone B has

a diameter of 9 inches and a slant height of 6 inches. How do their surface

areas compare?


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Name _____________________________________________ Date ____________________

Walk in the Footsteps of Archimedes Volume and Surface Area of a Sphere

VocabularyDescribe the similarities and differences between each term.

1. radius of a sphere and diameter of a sphere

2. diameter of a sphere and antipodes of a sphere

3. cross section of a sphere and great circle of a sphere

4. surface area of a sphere and annulus

5. hemisphere and sphere


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Problem SetCalculate the volume of each sphere. Use 3.14 for �. Round decimals to the nearest tenth, if necessary.

1. r � 7 m 2. r � 6 in.

r r

V � 4 __ 3 �r 3

V � 4 __ 3 �(7)3

V � 1372 _____ 3 �

V � 1436.0 m3

3. d � 20 in. 4. d � 16 m

d d

5. r � 2.5 cm 6. r � 11.25 mm

r r


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7. The radius of the great circle of a sphere is 8 meters.

8. The radius of the great circle of a sphere is 12 feet.

9. The diameter of the great circle of a sphere is 20 centimeters.

10. The diameter of the great circle of a sphere is 15 yards.


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Calculate the surface area of each sphere. Use 3.14 for �. Round decimals to the nearest tenth, if necessary.

11. r � 4 m 12. r � 6 in.

r r

SA � 4�r 2

SA � 4�(4)2

SA � 64�

SA � 201.0 m2

13. d � 11 m 14. d � 9 in.

d d

15. r � 2.5 in. 16. r � 3.25 in.

r r


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17. The radius of the great circle of a sphere is 5 feet.

18. The radius of the great circle of a sphere is 17 meters.

19. The diameter of the great circle of a sphere is 18 yards.

20. The diameter of the great circle of a sphere is 3 meters.

Calculate the volume of each sphere given its surface area. Use 3.14 for �. Round decimals to the nearest ten-thousandth, if necessary.

21. The surface area of a sphere is 8 square meters.

SA � 4�r 2 V � 4 __ 3 �r 3

8 � 4�r 2 V � 4 __ 3 �(0.7891)3

0.6369 � r 2 V � 2.1283 m3

0.7981 � r


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22. The surface area of a sphere is 3 square feet.

23. The surface area of a sphere is 10 square inches.

24. The surface area of a sphere is 2 square centimeters.

25. The surface area of a sphere is 12 square meters.

26. The surface area of a sphere is 1 square millimeter.

match each term to its corresponding definition. · 2011-11-07 · 5. 6. calculate the surface area...

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