The radius of a sphere is given by r=(3v/4pi)^1/3. Find the radius if the volume is 36pi cubic feet.

Answer 1

r - radius of the sphere

V - volume of the sphere

r = (3V/4π)^1/3 ← given

V = 36π ← given

Substituting the value for volume in the formula for radius:

r = (3 • 36π/4π)^1/3 = (3³)^1/3 = 3

Answer 2

The volume of a sphere is given by

V = 4/3 π r^3

Solving for r, gives the equation in the problem

r = (3V/4π)^1/3

If the volume is 36π, then

36π = 4/3 π r³

Divide both sides by π, which leaves

36 = 4/3 r³

Divide both sides by 4/3 (or multiply both sides by 3/4

27 = r³

Finally, find the cube root of both sides

r = 27^1/3= 3

The radius = 3.