Asphere 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