Question

Two similar solids have a scale factor of 3:4. What is the ratio of their volumes, expressed in lowest terms?

Answer 1

The ratio of their volumes is equal to
`(27)/(64)`

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 dilated figure

y-------> the volume of the original figure

so

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

we have

`z=(3)/(4)`

substitute

`((3)/(4))^(3)=(x)/(y)`

`((27)/(64))=(x)/(y)`

therefore

The ratio of their volumes is equal to
`(27)/(64)`

Answer 2

The ratio of the volumes will be equal to the ratio of the cubes of the sides. Thus:
Volume ratio:
3³: 4³
27 : 64