Volume of rectangular prisms

Rectangular prisms

Volume is the amount of space inside a 3-dimensional figure. It is measured in cubic units. A cubic centimeter is a cube that is 1 cm wide, 1 cm long, and 1 cm high.

Another way to think of volume is to find the number of unit cubes necessary for building the figure.

 


Example 1

Suppose this is a cubic unit:

How many cubic units would be needed to build this object?

[show answer]

 


Example 2

How many unit cubes are needed to build this object?

[show answer]

 


Example 3

How many cubes are in this figure?

[show answer]

 

Example 3 shows us that a shortcut for finding the volume of a rectangular prism is to find the number of cubes on the bottom "floor" and the multiply by the number of floors.

Volume = (number of cubes on the bottom floor) x (number of floors)
Volume = Area of the base x height
Volume = l • w • h



 

 


Let's practice this shortcut with a few more examples...

Example 4

Find the volume of this rectangular prism.

Volume = (Area of the base) • (height)
Volume = (4 • 3) • 5
Volume = 60 $\mbox{cm}^3$

(If you look at each layer, there are 12 cubes in each. There are 5 layers, so that would make a total of 60 cubes.)

 


Example 5

Find the volume.

[show answer]

 


Example 6

Find the volume.

[show answer]

 

 


 

Self-Check


Question 1

Find the volume of this prism.

 

[show answer]


Question 2

Find the volume.

 

[show answer]


Question 3

Find the volume.

 

[show answer]