Name_____________________________________ Class____________________________ Date________________
Lesson 11-4
Volumes of Prisms and Cylinders
Lesson Objectives
1 Find the volume of a prism
2 Find the volume of a cylinder
NAEP 2005 Strand: Measurement
Topic: Measuring Physical Attributes
Local Standards: ____________________________________
Vocabulary and Key Concepts.
All rights reserved.
Theorem 11-5: Cavalieri’s Principle
If two space figures have the same height and the same cross sectional area
at every level, then they have the same
.
Theorem 11-6: Volume of a Prism
The volume of a prism is the product of the
and the
h
.
B
V
Theorem 11-7: Volume of a Cylinder
The volume of a cylinder is the product of the
and the
h
.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
V Bh, or V B
r
Volume is
A composite space figure is
Examples.
1 Finding Volume of a Cylinder Find the volume of the cylinder.
Leave your answer in terms of π.
The formula for the volume of a cylinder is
The diagram shows h and d, but you must find r.
r 5 12d 5
V5
5p?
Use the formula for the volume of a cylinder.
?
5
9 ft
16 ft
Substitute.
Simplify.
The volume of the cylinder is
Daily Notetaking Guide
.
ft3.
Geometry Lesson 11-4
215
Name_____________________________________ Class____________________________ Date ________________
2 Finding Volume of a Triangular Prism Find the volume of the prism.
The prism is a
29 m
with triangular bases. The
base of the triangular prism is a
is the
where one leg
and the other leg is the
40 m
. Use the
20 m
Pythagorean Theorem to calculate the length of the other leg.
2
2
(
)(
The area B of the base is 21bh 12
area of the base to find the volume of the prism.
V
)
. Use the
All rights reserved.
Use the formula for the volume of a prism.
V
?
Substitute.
V
Simplify.
m 3.
The volume of the triangular prism is
3 Finding Volume of a Composite Figure Find the volume
25
cm
(
Volume of Prism II Bh (
Volume of Prism III Bh (
?
Sum of the volumes ?
?
)?
)?
)?
The volume of the composite space figure is
216
Geometry Lesson 11-4
10 cm
6 cm
cm
Each prism’s volume can be found using the formula V Volume of Prism I Bh 4 cm
.
cm3.
Daily Notetaking Guide
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
cm
4 cm
6 cm
6 cm
6 cm
cm
6 cm
cm
cm
6 cm
14 cm
to find the volume.
10 cm
You can use three
cm
of the composite space figure.
Name_____________________________________ Class____________________________ Date ________________
Quick Check.
1. Find the volume of the triangular prism.
10 m
5m
All rights reserved.
6m
2. The cylinder shown is oblique.
a. Find its volume in terms of π.
16 m
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
8m
b. Find its volume to the nearest tenth of a cubic meter.
3. Find the volume of the composite space figure.
2 in.
4 in.
2 in.
4 in.
Daily Notetaking Guide
Geometry Lesson 11-4
1 in.
217