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

Answer 2

Answer:

The ratio of their volumes is equal to $\frac{27}{64}$

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 dilated figure

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

so

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

we have

$z=\frac{3}{4}$

substitute

$(\frac{3}{4})^{3}=\frac{x}{y}$

$(\frac{27}{64})=\frac{x}{y}$

therefore

The ratio of their volumes is equal to $\frac{27}{64}$