Question

A sphere has a volume of V=576 in3. Find its surface area.

Answer 1

V = (4/3) × pi × r^3
A = 4 × pi × r^2

These formulas share "r" in common, so a good idea would be to solve for r using the formula for V since we are given the volume.

576 = (4/3)×pi×r^3
576 × (3/4) = pi×r^3
576 × (3/4) / pi = r^3
(576 × 3/4 / pi)^(1/3) = r
(notice that (r^3)^(1/3) = r)
432 / pi = r

Since r^2 is in the surface area formula, let's solve for that.
r = 432 / pi
r^2 = (432/pi)^2
= 432^2 / pi^2
= 186624 / pi^2

A = 4 × pi × r^2
= 4 × pi × (186624 / pi^2)
= 4 × 186624 × (pi / pi^2)
= 4 × 186624 × (1 / pi)
= 4 × 186624 / pi
= 237617.0568 in^2

Answer 2

Volume = (4/3) × π × r3 cubic units
Area = 4 × π × r2 square units.