Question

How will the volume of the prism change if each side is increased by a factor of 4?

Answer 1

The volume will be 64 times the original volume.

Explanation:

Answer 2

the new volume of the prism is
`64` times the original volume

Explanation:

we know that

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

Let

z------> the scale factor

x------> the volume of the dilated prism

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

so

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

In this problem we have

`z=4`

substitute

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

`64=(x)/(y)`

`x=64y`

that means-----> the new volume of the prism is
`64` times the original volume