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?

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

Answered by AL2006 | 2024-06-10

The volume of the enlarged rectangular prism is 6720 m³. This is calculated by multiplying the original volume (105 m³) by the cube of the scale factor (4), which is 64. Therefore, the new volume is 64 times the original volume.
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Answered by AL2006 | 2024-12-23