What is the surface area of a sphere if its volume is 288π cubic inches? leave your answers in terms of π. a. 216π in² b. 144π in² c. 288π in² d. 16π in²

Remark

The Volume of a sphere is V = (4/3) pi r^3. From that, you need to find r.

Givens

V = 288*pi

Substitute

288 pi = (4/3) pi r^3 Divide both sides by pi

288 pi/pi = (4/3) pi r^3 / pi

288 = (4/3) r^3 Multiply by 3

288*3 = 4*r^3

864 = 4r^3 Divide by 4

864 / 4 = 4 r^3 / 4

216 = r^3

Take the cube root of both sides.

cube_root(r^3) = cube_root(216)

r = 6

Surface Area

Formula

Area = 4 pi r^2

Substitute

r = 6

Area = 4 * pi * 6^2

Area = 4*36 * pi

Area = 144 pi Answer