A sphere and a cylinder have the same radius and height. The volume of the cylinder is 64 m^3. What is the volume of the sphere?

A. 64/3 m^3

B. 32 m^3

C. 128/3 m^3

D. 64 m^3

The correct answer is C) 128/3 m^3.

The formula for the volume of a sphere is V=4/3πr³.

The formula for the volume of a cylinder is V=πr²h.

Since the cylinder and the sphere have the same height:

The "height" of the sphere is the same as the diameter. This means the height of the cylinder is equal to the diameter of the sphere, or 2 times the radius:

h=2r

Plugging this into our formula for the volume of a cylinder, along with the actual volume, we have:

V=πr²h

64=πr² (2r)

64=2πr³

Dividing both sides by 2π, we have

64/2π = r³

32/π = r³

Plugging this into our formula for the volume of a sphere:

V=4/3πr³

V = (4/3) π (32/π)

V=128π/3π

V=128/3