surface area (SA) is 4×pi×r^2, where pi=3.14 and r=radius
Since you didn't give any relationship between a larger and smaller sphere, here are some examples:
1) if the volume (v) of a larger sphere (R) is 10 times the volume of a smaller (r)
Then v (R) = 10× v (r), and v = 4/3×pi×r^3, so:
4/3×3.14×R^3 = 10 (4/3×3.14×r^3)
But SA = 4×3.14×r^2
So convert v into SA: v×3/r = SA
So SA (R) = 3/r (10×4/3×3.14×r^3)
The r^3 / r can be reduced to r^2, and then 3×10×4/3 = 10×4 = 40
Thus the surface area of the larger sphere is 40 times the surface area of the smaller
2) if the radius of the larger (R) is 10 times the smaller (r)
Then R = 10r, SA = 4×pi×r^2
So SA (R) in terms of r is:
SA (R) = 10 (4×3.14×r^2)
SA = 10×4×3.14r^2 = 125.6r^2
So in this case the surface area of the larger sphere is 126 times the surface area of the smaller sphere
I hope that didn't confuse you too much!!
