Name ________________________________________ Date __________________ Class__________________
LESSON
10-7
Reteach
Volume of Pyramids and Cones
Volume of a Pyramid
The volume of a pyramid with base area B
and height h is
1
V = Bh .
3
Volume of a Cone
The volume of a cone with base area B,
radius r, and height h is
1
1
V = Bh , or V = πr 2 h .
3
3
Find the volume of each pyramid. Round to the nearest tenth
if necessary.
1.
2.
_________________________________________
________________________________________
Find the volume of each cone. Give your answers both in terms of π
and rounded to the nearest tenth.
3.
4.
_________________________________________
________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
10-54
Holt Geometry
Name ________________________________________ Date __________________ Class__________________
LESSON
10-7
Reteach
Volume of Pyramids and Cones continued
The radius and height of the cone are
1
multiplied by . Describe the effect on
2
the volume.
new volume, dimensions multiplied by
original volume:
V=
=
1 2
πr h
3
1
2
π ( 4) (6)
3
= 32π in3
V=
1
:
2
1 2
πr h
3
1
2
π ( 2) (3 )
3
r = 4, h = 6
=
Simplify.
= 4π in3
r = 2, h = 3
Simplify.
3
1
1
⎛ 1⎞
If the dimensions are multiplied by , then the volume is multiplied by ⎜ ⎟ , or .
2
8
⎝2⎠
Describe the effect of each change on the volume of the given figure.
5. The dimensions are doubled.
6. The radius and height are multiplied by
_________________________________________
1
.
3
________________________________________
Find the volume of each composite figure. Round to the nearest tenth if necessary.
7.
8.
_________________________________________
________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
10-55
Holt Geometry
LESSON 10-7
Practice A
1. V =
1
Bh
3
1 2
πr h
3
2. V =
3. V = 24 m3
4. Possible answer:
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
3
6. V ≈ 257.1 ft3
7. V ≈ 201.1 in3
8. V = 60 mm3
Reteach
3
8. V ≈ 2.1 in
5. V ≈ 2814.9 m3
9. V = 2916π mm
1. V = 35 in3
10. V = 108π mm3
2. V ≈ 213.3 mm3
3. V = 64π ft3 ≈ 201.1 ft3
11. The volume is divided by 27.
4. V = 33π cm3 ≈ 103.7 cm3
12. V = 15 ft3
5. The volume is multiplied by 8.
Practice B
6. The volume is multiplied by
1. V ≈ 3934.2 mm3
2. V = 56 yd3
7. V = 126 cm3
3. 4,013,140 ft3
4. V = 80π cm3; V ≈ 251.3 cm3
5. V = 25,088π mi ; V ≈ 78,816.3 mi
3
1. rectangle ABDC
3
6. V = 4.5π m ; V ≈ 14.1 m
2. rectangular pyramid 3. V =
7. The volume of the cone is one-third the
volume of the cylinder.
8. The volume is multiplied by
8
.
27
10. V ≈ 21.4 ft
5. 8 units
6. 10 units
7. V = 320 units3
10. 100 units
3
11. V ≈ 123.7 mm
1
Bh
3
4. 12 units
8. square LMNP
9. The volume is multiplied by 27.
3
8. V ≈ 301.6 in3
Challenge
3
3
1
.
27
2
9. 10 units
11. octahedron
12. Consider the octahedron as two square
pyramids with different altitudes, h1 and
1
h2. V = B(h1 + h2) Note that altitude is
3
always a positive number.
Practice C
1. Possible answer: A square pyramid with
height equal to an edge length has onethird the volume of a cube with the same
edge length.
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
2. 3 + 3 5 ; 9.7
Reading Strategies
3. 3 + 3 2 ; 7.2
1. V ≈ 3141.6 cm3
2. V = 28 ft3
3. V ≈ 277.3 in3
4. V ≈ 3534.3 ft3
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A32
Holt Geometry