Two spheres have volumes of 8π cm3 and 64π cm3. If the surface area of the smaller sphere is 16π cm2, what is the surface area of the larger sphere?

64π cm2

96π cm2

128π cm2

256π cm2

Think of it as a ratio:

Volumes:

8pi : 64pi

Area:

16pi : x

For the volumes, going from 8pi to 64pi requires multiplying 8pi by 8; multiplying by 8, therefore, is the volumetric scale factor, but we want to find the s' area of the larger sphere from the s' area of the smaller one;

we need the s' area scale factor.

To get this, we need to cube root the volumetric scale factor and then square it so:

8^1/3 = 2

2^2 = 4

Area scale factor = 4

so the area of the larger sphere is:

16 * 4 = 64 cm^2

If you don't get the scale factor stuff leave a comment and I'll try my best to elaborate.