Question

Two similar solids have a scale factor of 6 : 7. What is the ratio of their volumes, expressed in lowest terms?

Answer 1

The ratio of volumes is equal to the ratio of the cubes of the scale factor. Thus,
Volume ratio:
6³ : 7³
216 : 343

Answer 2

Answer:

The ratio of their volumes is equal to $\frac{216}{343}$  

Step-by-step explanation:

we know that

If two solids are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x/y----> the ratio of its volumes

so

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

we have

$z=\frac{6}{7}$

substitute

$(\frac{6}{7})^{3}=\frac{x}{y}$

$(\frac{216}{343})=\frac{x}{y}$

rewrite

$\frac{x}{y}=(\frac{216}{343})$ -----> the fraction is irreducible