1. Volumes of Rectangular Prisms and Cylinders
Lesson 9-9

2. 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.

3. 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.

4. 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.)

5. 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 cm3
Volume gives us cubic units.

6. Volume of a Cylinder V = Bh V = (r2) x h V = (3.14)(52)(16)
In this case, the base is a circle. The area formula for a circle is r2
5 in
16 in
V = (r2) x h
V = (3.14)(52)(16)
V = (3.14)(25)(16)
V = 1,256 in3

7. Homework Time
V = l w h