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