Question

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

Answer 1

Answer:

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

$27$

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 enlarged prism

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

so

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

we have

$z=3$

$y=24\ in^{3}$

substitute

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

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

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

$3^{3}=27$

Verify

$\frac{648}{24}=27$ -----> is correct