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.

You are watching: How many cubes are in a rectangular prism

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:

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

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Example 2

How many unit cubes are needed to build this object?

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Example 3

How many cubes are in this figure?


There are 6 cubes on the bottom "floor"

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There are also 6 cubes on the second "floor"

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And there are 6 cubes on the third (top) "floor"

So, there are 18 cubes in this figure.


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.

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Volume = (Area of the base) • (height) Volume = (4 • 3) • 5 Volume = 60 $mboxcm^3$

(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.

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Volume = l • w • h

Volume = 6 • 3 • 3

Volume = 36 cubic units


Example 6

Find the volume.

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V = l • w • h

V = 5 • 4 • 7

V = 140 units cubed


Self-Check

Question 1

Find the volume of this prism.

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$large~24mbox u^3$


Question 2

Find the volume.

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$large~42mbox cm^3$


Question 3

Find the volume.

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$large~48mbox cm^3$


‹ Surface area of rectangular prisms up Volume of cylinders ›

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