Question

The two rectangular prisms are similar.

Answer 1

Answer:

The volume of the larger rectangular prism is $648\ cm^{3}$

Step-by-step 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

$z^{3}=\frac{x}{y}$

In this problem we have

$z=\frac{12}{4}=3$ ---> the scale factor is equal to the ratio of its corresponding sides

$y=24\ cm^{3}$

substitute and solve for x

$3^{3}=\frac{x}{24}$

$x=27*24=648\ cm^{3}$