Question

A prism with a volume of 3125 ft³ is scaled down to a volume of 200 ft³.

What is the scale factor?
Enter your answer, as a decimal or a fraction in simplest form, in the box.

I think it's 2/5 or 0.4

Answer 1

the right answer is 2/5

Answer 2

The scale factor is equal to
`0.4` or
`(2)/(5)`

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 dilated prism

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

so

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

we have

`x=200\ ft^(3)`

`y=3,125\ ft^(3)`

substitute

`z^(3)=(200)/(3,125)`

`z=\sqrt[3]{(200)/(3,125)}`

`z=0.4` or
`z=(2)/(5)`