Question

If the ratio of the volumes of two similar solids is 8:125, then what is the ratio of their surface areas?

Answer 1

well, we can compare the volumes of a cube ot that of a square ...

Answer 2

a cube of side cbrt(8) and a cube of side sqrt(125)

the squares have areas of (cbrt(8))^2 and (cbrt(125))^2

Answer 3

what about cones?

V = 4/3 pi r^3

8V = 4/3 pi (r cbrt(8))^3

A = 4 pi (r cbrt(8))^2 same ratio

Answer 4

I still don't understand.

Answer 5

the squares have areas of (cbrt(8))^2 and (cbrt(125))^2

what more is there to say?

Answer 6

I just don't get it. Why are you using squares?

Answer 7

@jim_thompson5910 You're good at explaining things.. Do you know the answer?