Question

The volumes of two spheres are in the ratio 64:27. Find the ratio of their surface areas

Answer 1

volume of a sphere (v)=4/3pi r3
v1/v2=64/27
r = radius of sphere
4/3pi r13 / 4/3pi r23=64/27
r13/r23=64/27
therefore
r1/r2=4/3

surface of sphere(A)=6r2
A1/A2=6r12/6r22
A1/A2=r12/r22
A1/A2= (4)2/(3)2
A1/A2=16/9