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Volumes of Rectangular Prisms and Cylinders

Lesson 9-9

Vocabulary

• The volume of a three-dimensional figure is the number of cubic units needed to fill the space inside the figure.

• A cubic unit is a cube that measures 1 unit long, 1 unit wide, and 1 unit high.

Counting Cubes

• If the figure is split into cubes already, then just count the cubes in one layer and multiply that by the number of layers.

The top layer is 4 x 5, or 20 cubic units.

There are 20 cubic units per layer, times 3 layers, for a volume of 60 cubic units.

Using Formulas

• To find the volume of a rectangular prism or a cylinder, multiply the area of the base by the height .

• Volume = Area of Base x height

• V = Bh

• (The capital B does not stand for base, it stands for area of the base.)

Volume of a Rectangular

Prism

V = Bh In this case, the base is a rectangle.

The area formula for a rectangle is l x w.

V = (l x w) x h

V = (4 x 3) x 12

V = 144 cm 3

Volume gives us cubic units.

Volume of a Cylinder

**5 in**

**16 in**

V = Bh

V = (

r 2 ) x h

V = (3.14)(5 2 )(16)

V = (3.14)(25)(16)

V = 1,256 in 3

In this case, the base is a circle.

The area formula for a circle is

r 2

Homework Time

V = l w h