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

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

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)=(x)/(y)`

In this problem we have

`z=(1)/(2)`

substitute

`((1)/(2))^(3)=(x)/(y)`

`((1)/(8))=(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