Name ________________________________________ Date __________________ Class __________________

Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

49

Volume Module Quiz: D

Use 3.14 for π. Round your answers to the nearest hundredth. 1. What is the volume of the cylinder below?

Use the formula π= 2 .V r h

A 31.4 in3 B 157 in3 C 62.8 in3

2. What is the volume of the cone below?

Use the formula π= 21 .3

V r h

A 133.97 in3 B 267.95 in3 C 33.49 in3

3. What is the measure of ∠C?

A 44° B 39° C 49°

4. What is the volume of the sphere below?

Use the formula π= 34 .3

V r

A 16.75 cm3 B 66.99 cm3 C 267.95 cm3

5. What is the volume of the cylinder below? Use the formula π= 2 .V r h

A 113.04 ft3 B 1,356.48 ft3 C 339.12 ft3

6. What is the volume of the sphere below?

Use the formula π= 34 .3

V r

A 339.12 cm3 B 3,052.08 cm3 C 37.68 cm3

MODULE

9

Name ________________________________________ Date __________________ Class __________________

Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

50

Volume

7. What is the volume of this cone? Use

the formula π= 21 .3

V r h Show your

work.

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8. The formula for the volume of a cone is

π= 21 .3

V r h Which part of the formula

represents the area of the base? How do you know?

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9. A cone has the same radius as a cylinder, and exactly the same height. Which has a greater volume, the cone or the cylinder? Explain how you know.

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10. Use the Pythagorean Theorem, + =2 2 2,a b c to find the measure of

the hypotenuse in this triangle. Show your work.

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11. An ice cream cone is made of a cone shape and half a sphere shape. Explain how you could find the volume of the entire ice cream cone.

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MODULE

9

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185

MODULE 9 Volume Module Quiz 9: B 1. B 2. D 3. A 4. B 5. C 6. D 7. B 8. B

9. 2(3.14)(1.75 )(1.25)V ≈ ≈ 312.02 in.V

2(3.14)(1.2 )(1.25)V ≈ ≈ 35.65 in.V

− = 312.02 5.65 6.37 in. difference 10. Entire funnel:

2 31 (3.14)(4.5 )(9) 190.76 in.3

V ≈ ≈

Tip: 2 31 (3.14)(0.5 )(1) 0.26 in.3

V ≈ ≈

190.76 − 0.26 = 190.5 in.3 11. No, the triangles have only one congruent

angle so they are not similar. The angles of the left triangle measure 60°, 58°, and 62°. The angles of the right triangle measure 60°, 59°, and 61°.

12. 713.21 3.14 227.14÷ = 25.2 27.04=

227.14 27.04 8.4÷ = The height is about 8.4 inches.

13. Two cylinders with the same diameter may or may not have the same volume, depending on the two heights. The same is true for two cones. Two spheres with the same diameter will have the same volume because the formula doesn’t use any other dimension.

14. No, 202 + 482 ≠ 542, so it cannot be a right triangle.

Module Quiz 9: D 1. C 2. A 3. B 4. C

5. C 6. B

7. 213

V r hπ=

21 (3.14)(2 )(18)3

V =

1 (3.14)(4)(18)3

V =

1 (3.14)(72)3

V =

1 (226.08)3

V =

= 375.36 in.V

8. Sample answer: The 2rπ part of the formula is the base. I know because that’s the formula for the area of a circle.

9. Sample answer: The cylinder has a greater volume. The formula for the volume of a cylinder is V = π r

2h, and the formula for the volume of a cone is

V = 13

π r

2h. So if a cone and cylinder

have the same height and radius, the

volume of the cone is 13

the volume of

the cylinder.

10. 2 2 2a b c+ = 2 2 26 8 c+ =

236 64 c+ = 2100 c= 2100 c= 10 c= The hypotenuse is 10 in. long.

11. Sample answer: Find the volume of the cone. Then find the volume of the sphere and divide it in half. Add the volume of the cone and the volume of half the sphere.

MODULE 10 Surface Area Module Quiz 10: B 1. D 2. B 3. D 4. C 5. D