10-2
10-2Volume
VolumeofofPrisms
Prismsand
andCylinders
Cylinders
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
22
10-2 Volume of Prisms and Cylinders
Warm Up
Identify the figure described.
1. two triangular faces and the other faces in the
shape of parallelograms
triangular prism
2. one hexagonal base and the other faces in the
shape of triangles hexagonal pyramid
3. one circular face and a curved lateral surface that
forms a vertex cone
Course 2
10-2 Volume of Prisms and Cylinders
Problem of the Day
How can you cut the rectangular prism into
8 pieces of equal volume by making only 3
straight cuts?
Course 2
10-2 Volume of Prisms and Cylinders
Learn to find the volume of prisms and
cylinders.
Course 2
10-2 Volume of Prisms and Cylinders
Vocabulary
volume
Course 2
10-2 Volume of Prisms and Cylinders
Any three-dimensional figure can be filled
completely with congruent cubes and parts of
cubes. The volume of a three-dimensional figure
is the number of cubes it can hold. Each cube
represents a unit of measure called a cubic unit.
Course 2
10-2 Volume of Prisms and Cylinders
Additional Example 1: Using Cubes to Find the
Volume of a Rectangular Prism
Find how many cubes the prism holds. Then
give the prism’s volume.
You can find the volume of
this prism by counting how
many cubes tall, long, and
wide the prism is and then
multiplying.
1 · 4 · 3 = 12
There are 12 cubes in the prism, so the volume is 12
cubic units.
Course 2
10-2 Volume of Prisms and Cylinders
To find a prism’s volume, multiply its
length by its width by its height.
4 cm
Course 2
4 cm · 3 cm · 1cm = 12 cm3
1 cm
length · width · height = volume
3 cm
area of
· height = volume
base
10-2 Volume of Prisms and Cylinders
Reading Math
Any unit of measurement with an exponent of 3
is a cubic unit. For example, cm3 means “cubic
centimeter” and in3 means “cubic inch.”
Course 2
10-2 Volume of Prisms and Cylinders
Check It Out: Example 1
Find how many cubes the prism holds. Then
give the prism’s volume.
You can find the volume of
this prism by counting how
many cubes tall, long, and
wide the prism is and then
multiplying.
2 · 4 · 3 = 24
There are 24 cubes in the prism, so the volume is 24
cubic units.
Course 2
10-2 Volume of Prisms and Cylinders
The volume of a rectangular prism is the
area of its base times its height. This
formula can be used to find the volume
of any prism.
VOLUME OF A PRISM
The volume V of a prism is the area of its base
B times its height h.
V = Bh
Course 2
10-2 Volume of Prisms and Cylinders
Additional Example 2A: Using a Formula to Find the
Volume of a Prism
Find the volume of the prism.
4 ft
4 ft
12 ft
V = Bh
Use the formula.
The bases are rectangles.
The area of each rectangular base is 12 · 4 = 48
V = 48 · 4
Substitute for B and h.
Multiply.
V = 192
The volume of the prism is 192 ft3.
Course 2
10-2 Volume of Prisms and Cylinders
Additional Example 2B: Using a Formula to Find the
Volume of a Prism
Find the volume of the prism.
V = Bh
Use the formula.
The base is a triangle.
The base is 1 · 3 · 4 = 6
2
V=6·6
Substitute for B and h.
Multiply.
V = 36
The volume of the prism is 36 cm3.
Course 2
10-2 Volume of Prisms and Cylinders
Check It Out: Example 2A
Find the volume of the prism.
6 ft
6 ft
8 ft
V = Bh
Use the formula.
The bases are rectangles.
The area of each rectangular base is 8 · 6 = 48
V = 48 · 6
Substitute for B and h.
Multiply.
V = 288
The volume to the nearest tenth is 288 ft3.
Course 2
10-2 Volume of Prisms and Cylinders
Check It Out: Example 2B
Find the volume of the prism.
5 in
1.5 in.
V = Bh
Use the formula.
The base is a triangle.
The base is 1 · 1.5 · 5 = 3.75
2
V = 3.75 · 4
Substitute for B and h.
Multiply.
V = 15
The volume of the prism is 15 in3.
Course 2
10-2 Volume of Prisms and Cylinders
Finding the volume of a cylinder is similar to finding
the volume of a prism.
VOLUME OF A CYLINDER
The volume V of a cylinder is the area of its base,
r2, times its height h.
V = r2h
Course 2
10-2 Volume of Prisms and Cylinders
Additional Example 3: Using a Formula to Find the
Volume of a Cylinder
Find the volume of a cylinder to the nearest
tenth. Use 3.14 for .
V = r2h
Use the formula.
The radius of the cylinder is 5 m, and
the height is 4.2 m
V  3.14 · 52 · 4.2 Substitute for r and h.
V  329.7
Multiply.
The volume is about 329.7 m3.
Course 2
10-2 Volume of Prisms and Cylinders
Check It Out: Example 3
Find the volume of a cylinder to the nearest
tenth. Use 3.14 for .
7m
3.8 m
V = r2h
Use the formula.
The radius of the cylinder is 7 m,
and the height is 3.8 m
V  3.14 · 72 · 3.8
Substitute for r and h.
V  584.668
Multiply.
The volume is about 584.7 m3.
Course 2
10-2 Volume of Prisms and Cylinders
Lesson Quiz: Part I
Find how many cubes the prism holds. Then
give the prisms volume.
1.
2.
48 cubic units
Course 2
792 cm3
10-2 Volume of Prisms and Cylinders
Lesson Quiz: Part II
3. A storage tank is shaped like a cylinder. Find
its volume to the nearest tenth. Use 3.14 for .
4,069.4 m3
Course 2