The volume of a right circular cylinder is

• A. 2 pi r h
• B. pi d^2 h
• C. pi r^2 h
• D. pi r h^2

Answer: (C)

Volume is found by multiplying the area of the base by the height for a right circular cylinder. The base is a circle with area πr^2, so the volume is πr^2 h. This uses the actual radius, and combines base area with how tall the cylinder is. If you use diameter instead of radius, you’d get πd^2h, which is four times too large since d = 2r. A height squared term, as in πr h^2, doesn’t fit the dimensional sense of volume, and 2πrh corresponds to the lateral surface area, not volume. So the correct expression is πr^2 h.