Question

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

Answer 1

216:343 or 216/343. Verified by correct test results.

Answer 2

The ratio of their volumes is equal to
`(216)/(343)`

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)=(x)/(y)`

we have

`z=(6)/(7)`

substitute

`((6)/(7))^(3)=(x)/(y)`

`((216)/(343))=(x)/(y)`

rewrite

`(x)/(y)=((216)/(343))` -----> the fraction is irreducible