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