Question

A rectangular solid is dilated by a factor of 0.5. How many times larger is the volume of the resulting solid than the volume of the original solid?

Answer 1

The volume of the resulting solid will be twice as large as the volume of the original solid.

Answer 2

Answer:

The volume of the resulting solid is eight times smaller than the volume of the original solid

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 resulting solid

y-----> the volume of the original solid

so

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

In this problem we have

$z=\frac{1}{2}$

substitute

$(\frac{1}{2})^{3}=\frac{x}{y}$

$(\frac{1}{8})=\frac{x}{y}$

$y=8x$

The volume of of the original solid is eight times larger than the volume of the resulting solid

or

$x=(1/8)y$

The volume of the resulting solid is eight times smaller than the volume of the original solid