Volume is the amount of room inside a 3-dimensional figure. It is measure up in cubic units. A cubic centimeter is a cube the is 1 centimeter wide, 1 cm long, and also 1 centimeter high.

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

Another method to think that volume is to uncover the variety of unit cubes essential for structure the figure.

Example 1

Suppose this is a cubic unit:

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How countless cubic systems would be needed to develop this object?

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Example 2

How many unit cubes are required to construct this object?

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Example 3

How many cubes space in this figure?


There space 6 cubes top top the bottom "floor"

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over there are additionally 6 cubes ~ above the 2nd "floor"

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And there room 6 cubes top top the 3rd (top) "floor"

So, there are 18 cubes in this figure.


Example 3 reflects us that a shortcut for recognize the volume that a rectangular prism is to uncover the number of cubes ~ above the bottom "floor" and the main point by the variety of floors.

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

Let"s exercise this shortcut with a couple of more examples...

Example 4

Find the volume the this rectangular prism.

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

(If you look at each layer, there room 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 = together • 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 devices cubed


Self-Check

Question 1

Find the volume that this prism.

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$\large~24\mbox u^3$


Question 2

Find the volume.

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$\large~42\mbox cm^3$


Question 3

Find the volume.

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$\large~48\mbox cm^3$


‹ surface ar area of rectangular prisms increase Volume the cylinders ›

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