Question

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

Answer 1

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