MSM07G7_RESBK_Ch10_019-027.pe
2/14/06
11:34 AM
Page 26
Name
LESSON
Date
Class
Reading Strategies
10-3 Use a Graphic Organizer
This chart will help you compare pyramids and cones and the
formulas for finding the volume of these figures.
Pyramid
Volume of Pyramid
• Base is a polygon.
1
Volume ! 3
• Faces are triangles.
•h
(B ! area of base)
• Vertex and base are at
opposite ends.
Pyramids and Cones
Cone
Volume of Cone
1
• Base is a circle.
Volume ! 3 !r 2 • h
• Has one curved surface.
(!r 2 ! area of base)
• Vertex is opposite the base.
Use the graphic organizer to answer each question.
a cone
a polon
a circle
1. Which figure has one curved surface?
2. What forms the base of a pyramid?
3. What forms the base of the cone?
4. What is the formula for the area of a cone’s base?
!r 2
5. What shape are the faces of a pyramid?
triangle
6. Compare the volume formulas. How are they alike?
1
3
In each you find !! of the area of the base multiplied by the height.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
26
Holt Mathematics
Reteach
LESSON
10-3 Volume of Pyramids and Cones (continued)
Challenge
LESSON
10-3 Take It Out
1
Sometimes you can find the volume of an oddly shaped figure by
first finding the volume of the entire solid and then subtracting a part
that is missing.
You can find the volume of a cone by using the formula V ! !3!Bh.
Find the volume of each cone to the nearest whole number.
2m
Find the volume of each figure. Round to the nearest whole
number.
8. The area of the base is
2
2
B ! !r ! 3.14 •
1
1
1
65
13
9. V ! !3! Bh ! !3! •
! !3! •
2
!
22
•
!
13
2
m
1.
2.
2m
2m
5m
5
m3
10 ft
6m
10.
B ! !r
2
2
5
B ! 3.14 •
4 yd
25
! 3.14 •
6m
!
79
yd
1
79
V ! !3! •
1
! !3! •
11.
316
V of cube:
4
•
105
!
8 ft
Cube with rectangular prism
removed
1
V ! !3!Bh
5 yd
8 ft
6m
2
216 m3
V of figure:
12.
213 ft3
V of missing part:
3
192 m
427 ft
V of figure:
3.
7 ft
640 ft3
V of prism:
24 m3
V of missing part:
yd3
Rectangular prism with pyramid
removed
4.
3
8 cm
8 cm
10 cm
6m
6m
10 ft
3 cm
12 cm
733 ft3
75 cm3
13.
Cube with 2 m " 2 m " 6 m corners
removed
14.
V of cube:
8 ft
9 cm
5 cm
216 m3
V of figure:
V of rectangular prism:
3
96 m
V of missing part:
7 ft
Rectangular prism with triangular
prism removed
V of missing part:
120 m3
960 cm3
240 cm3
720 cm3
V of figure:
6 cm
339 cm3
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
469 ft3
23
Holt Mathematics
Write the correct answer.
2.The Great Pyramid in Egypt has a
square base that measures 751 feet
on each side. The pyramid is 481 feet
high. What is the volume of the Great
Pyramid? Round your answer to the
nearest cubic foot.
This chart will help you compare pyramids and cones and the
formulas for finding the volume of these figures.
Pyramid
3. A waffle cone that holds ice cream is
15 centimeters high and has a
diameter of 10 centimeters. What
volume of ice cream can it hold if it is
filled to the top?
1
Volume ! 3
• Faces are triangles.
•h
(B ! area of base)
• Vertex and base are at
opposite ends.
4. The base of a rectangular prism is
congruent to the base of a pyramid.
The height of the pyramid is 3 times
the height of the prism. Which figure
has a greater volume? Explain.
392.5 cm3
Volume of Pyramid
• Base is a polygon.
90,428,160 ft3
94.2 mL
Holt Mathematics
Reading Strategies
LESSON
10-3 Use a Graphic Organizer
Problem Solving
LESSON
10-3 Volume of Pyramids and Cones
1. Each of the cone-shaped cups
near the water cooler has a radius
of 3 centimeters and a height of
10 centimeters. If 1 cubic centimeter
can hold 1 milliliter of liquid, how
much water can each cup hold?
24
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Pyramids and Cones
Cone
Volume of Cone
1
The figures have the same
• Base is a circle.
Volume ! 3 !r 2 • h
volume. V (prism) ! Bh ;
1
V (pyramid) ! (!! Bh) • 3 ! Bh
• Has one curved surface.
(!r 2 ! area of base)
• Vertex is opposite the base.
3
Choose the letter of the correct answer.
5. A teepee that is shaped like a cone
has a diameter of 12 feet and a
height of 15 feet. What is the volume
of the teepee?
C 1,695.6 ft3
!
A 565.2 ft3
B 706.5 ft3
D 2,119.5 ft3
6. The top of a 44-story office building
is shaped like a pyramid. The base
of the pyramid is a right triangle with
the two legs measuring 73 feet and
78 feet. The pyramid is 35 feet high.
What is the volume of the pyramid?
F 199,290 ft3
H 41,756 ft3
G 66,430 ft3
!
J 33,215 ft3
G 96 cm3
25
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a cone
a polygon
a circle
1. Which figure has one curved surface?
2. What forms the base of a pyramid?
3. What forms the base of the cone?
4. What is the formula for the area of a cone’s base?
!r 2
5. What shape are the faces of a pyramid?
8. A square pyramid mold for a candle
has a base of 64 square centimeters
and a height of 12 centimeters. How
much greater is the volume of a
rectangular prism mold with the
same base and height?
F 64 cm3
H 256 cm3
7. The diameter of a cone-shaped
container is 4 inches. Its height is
6 inches. How much greater is the
volume of a cylinder-shaped
container with the same diameter
and height?
A 50.24 in3
C 100.98 in3
!
B 75.36 in3
D 200.96 in3
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Use the graphic organizer to answer each question.
triangle
6. Compare the volume formulas. How are they alike?
1
3
In each you find !! of the area of the base multiplied by the height.
!
J 512 cm3
Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
50
26
Holt Mathematics
Holt Mathematics