1 / 20

Warm Up

Problem of the Day

Lesson Presentation

Warm Up Identify the figure described. 1. two

triangular faces and the other faces in the shape

of parallelograms 2. one hexagonal base and the

other faces in the shape of triangles 3. one

circular face and a curved lateral surface that

forms a vertex

triangular prism

hexagonal pyramid

cone

Problem of the Day How can you cut the

rectangular prism into 8 pieces of equal volume

by making only 3 straight cuts?

Learn to find the volume of prisms and cylinders.

Vocabulary

volume

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.

Additional Example 1 Using Cubes to Find the

Volume of a Rectangular Prism

Find how many cubes the prism holds. Then give

the prisms 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.

To find a prisms volume, multiply its length by

its width by its height.

4 cm 3 cm 1cm 12 cm3

length width height volume

area of base

height volume

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.

Check It Out Example 1

Find how many cubes the prism holds. Then give

the prisms 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.

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

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.

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.

V 6 6

Substitute for B and h.

Multiply.

V 36

The volume of the prism is 36 cm3.

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.

Check It Out Example 2B

Find the volume of the prism.

5 in

4 in.

1.5 in.

V Bh

Use the formula.

The base is a triangle.

V 3.75 4

Substitute for B and h.

Multiply.

V 15

The volume of the prism is 15 in3.

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

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.

Check It Out Example 3

Find the volume of a cylinder to the nearest

tenth. Use 3.14 for ?.

7 m

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.

Lesson Quiz Part I

Find how many cubes the prism holds. Then give

the prisms volume.

1.

2.

48 cubic units

792 cm3

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