Question

If the ratio of the radii of two spheres is 3 : 10, what is the ratio of the surface areas of the two spheres?

A. 9 : 100
B. 3r2π : 10r2π
C. 27 : 1000
D. 3 : 10

Answer 1

Surface area for a sphere is 4 pi R^2

So for this example if the two Radii are 3:10 the ratio would be:

4 PI 3^2 : 4 PI 10^2
Reducing terms yields
9:100
Or answer A...

Answer 2

The square of the scale factor of two similar solids is the ratio of their areas.

(3/10)^2 = 9/100 is sthe ratio of their surface areas.