Question

A rectangular prism has a volume of 24 in³. For a school project, Sharon applies a scale factor of 3 to the prism.

Find the volume ratio of the enlarged prism to the original prism.

Enter your answer in the box in simplified form.

Answer 1

The volume ratio of the enlarged prism to the original prism is equal to

`27`

Explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z------> the scale factor

x-----> the volume of the enlarged prism

y-----> the volume of the original prism

so

`z^(3)=(x)/(y)`

we have

`z=3`

`y=24\ in^(3)`

substitute

`3^(3)=(x)/(24)`

`x=(27)(24)=648\ in^(3)` -----> volume of the enlarged prism

the volume ratio of the enlarged prism to the original prism is equal to

`3^(3)=27`

Verify

`(648)/(24)=27` -----> is correct