Finding the volume of a sphere with the surface are of a cylinder

Question

A sphere and a cylinder have the same radius. The height of the cylinder is twice as

long as the radius. If the surface area of the cylinder is 1350π, find the volume of the sphere

Answer 1

The formula for the surface area of a cylinder is:

SA = 2 * π * r² + 2 * π * r * h

We know that the surface area is 1350π and the height is twice the radius, so we can rewrite this and solve for the radius:

1350π = 2 * π * r² + 2 * π * r * (2r)

1350π = 6 * π * r²

r = 15

So the radius of the cylinder is 15. We are told the sphere has the same radius, so using the formula for the volume of a sphere, we can find the volume:

V = 4/3 * π * r³

V = 4/3 * π * 15³

V = 4500π