What is the volume of the enlarged prism?
The volume of the new prism is 6,720 m³ !
Heres 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).
Thats 8 times the original volume.
Where did the 8 come from?
Its 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).
Thats 64 times the original volume.
Where did the 64 come from?
Its the cube of 4.
We didnt 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.
Thats a good thing to remember.
The original volume was 105 m³.
The new volume is (4³) x (105) = (64) x (105) = 6,720 m³