A rectangular prism has a volume of 105 m3. This prism is enlarged using a scale factor of 4.

What is the volume of the enlarged prism?

Explain.

The volume of the new prism is 6,720 m³ !

Here’s how it works:

The volume of any rectangular prism is (length x width x height).

If you double each dimension, then  the new volume is

(2 x length) x (2 x width) x (2 x height) = 8 x (length x width x height).
That’s 8 times the original volume.
Where did the ’ 8 ’ come from?
It’s the cube of 2.

In this problem, we multiplied each dimension by 4, so the new volume is

(4 x length) x (4 x width) x (4 x height) = 64 x (length x width x height).
That’s 64 times the original volume.
Where did the ’ 64 ’ come from?
It’s the cube of 4.
We didn’t really have to figure it out.   We knew that if you multiply each dimension
by the same number, then you multiply the volume by the cube of that number.
That’s a good thing to remember.

The original volume was 105 m³.

The new volume is (4³) x (105) = (64) x (105) = 6,720 m³

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