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^3B. 32 m^3C. 128/3 m^3D. 64 m^3
Accepted Solution
A:
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