Question

The two rectangular prisms are similar.

What is the volume of the larger rectangular prism?

648 cm³

216 cm³

192cm³

72 cm³

Answer 1

648 cm³

I took the quiz. I hope this helps :)

Answer 2

The volume of the larger rectangular prism is
`648\ cm^(3)`

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 larger rectangular prism

y-----> the volume of the smaller rectangular prism

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

In this problem we have

`z=(12)/(4)=3` ---> the scale factor is equal to the ratio of its corresponding sides

`y=24\ cm^(3)`

substitute and solve for x

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

`x=27*24=648\ cm^(3)`