Name ________________________________________ Date __________________ Class__________________

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

10-52 Holt Geometry

Practice B Volume of Pyramids and Cones

Find the volume of each pyramid. Round to the nearest tenth if necessary.

1. 2.

the regular pentagonal pyramid the rectangular right pyramid

_________________________________________ ________________________________________

3. Giza in Egypt is the site of the three great Egyptian pyramids. Each pyramid has a square base. The largest pyramid was built for Khufu. When first built, it had base edges of 754 feet and a height of 481 feet. Over the centuries, some of the stone eroded away and some was taken for newer buildings. Khufu’s pyramid today has base edges of 745 feet and a height of 471 feet. To the nearest cubic foot, find the difference between the original and current volumes of the pyramid.

_________________________________________________________________________________________

Find the volume of each cone. Give your answers both in terms of π and rounded to the nearest tenth.

4. 5.

_________________________________________ ___________________________________________

6. a cone with base circumference 6π m and a height equal to half the radius ___________________________________

7. Compare the volume of a cone and the volume of a cylinder with equal height and base area.

_________________________________________________________________________________________

Describe the effect of each change on the volume of the given figure. 8. 9.

The dimensions are multiplied by 23

. The dimensions are tripled.

_________________________________________ ________________________________________

Find the volume of each composite figure. Round to the nearest tenth.

10. 11.

_________________________________________ ________________________________________

LESSON

10-7

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

A32 Holt Geometry

LESSON 10-7

Practice A

1. V = 13

Bh 2. V = 13

πr2h

3. V = 24 m3 4. V = 20 mi3

5. V = 400 in3

6. V = 8π km3; V ≈ 25.1 km3

7. V = 187.5π yd3; V ≈ 589.0 yd3

8. V ≈ 2.1 in3 9. V = 2916π mm3

10. V = 108π mm3

11. The volume is divided by 27. 12. V = 15 ft3

Practice B 1. V ≈ 3934.2 mm3

2. V = 56 yd3 3. 4,013,140 ft3

4. V = 80π cm3; V ≈ 251.3 cm3

5. V = 25,088π mi3; V ≈ 78,816.3 mi3

6. V = 4.5π m3; V ≈ 14.1 m3

7. The volume of the cone is one-third the volume of the cylinder.

8. The volume is multiplied by 827

.

9. The volume is multiplied by 27. 10. V ≈ 21.4 ft3 11. V ≈ 123.7 mm3

Practice C 1. Possible answer: A square pyramid with

height equal to an edge length has one-third the volume of a cube with the same edge length.

2. 3 + 3 5 ; 9.7 3. 3 + 3 2 ; 7.2

4. Possible answer: 5. V ≈ 2814.9 m3 6. V ≈ 257.1 ft3

7. V ≈ 201.1 in3 8. V = 60 mm3

Reteach 1. V = 35 in3 2. V ≈ 213.3 mm3 3. V = 64π ft3 ≈ 201.1 ft3 4. V = 33π cm3 ≈ 103.7 cm3

5. The volume is multiplied by 8.

6. The volume is multiplied by 127

.

7. V = 126 cm3 8. V ≈ 301.6 in3

Challenge 1. rectangle ABDC

2. rectangular pyramid 3. V = 13

Bh

4. 12 units 5. 8 units 6. 10 units 7. V = 320 units3

8. square LMNP 9. 10 units 10. 100 units2 11. octahedron 12. Consider the octahedron as two square

pyramids with different altitudes, h1 and

h2. V = 13

B(h1 + h2) Note that altitude is

always a positive number. 13. V ≈ 433.3 units3

Problem Solving 1. V ≈ 940.0 m3 2. V = 50.75π cm3

3. V ≈ 210.8 cm3 4. V = 98π in3

5. A 6. G 7. A

Reading Strategies 1. V ≈ 3141.6 cm3 2. V = 28 ft3 3. V ≈ 277.3 in3 4. V ≈ 3534.3 ft3