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

Volume = (4/3) * π * r 3 cubic units

Area = 4 * π * r 2 square units.

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