The volume of a cylinder with radius r and height h is which expression?

• A. v = 2πrh
• B. v = π r h
• C. v = π r^2 h
• D. v = 4/3 π r^3

Answer: (C)

Think of a cylinder as a prism with a circular base. The base area is A = πr^2. If you fill the cylinder with many thin disks of height dh, each disk has volume dV = base area × dh = πr^2 dh. Adding up all those disks from 0 to h gives V = πr^2 h. So the volume is base area times height.

That’s why the correct expression is π r^2 h. The other forms don’t represent volume: 2πrh is the lateral surface area of a cylinder, πrh mixes a length and a height to give an area, and 4/3 πr^3 is the volume of a sphere.