What is the standard formula for the volume of a cylinder?

• A. V = π r^2 h
• B. V = 2 π r h
• C. V = π d^2 h
• D. V = π r^2

Answer: (A)

Volume is found by multiplying the area of the circular base by the cylinder’s height. The base area is πr^2, so the volume is V = πr^2 h. Think of filling the cylinder with many thin discs whose areas are πr^2 and stacking them to the full height h.

The other expressions aren’t volumes: 2πrh is the curved surface area around the sides; πd^2h uses diameter instead of radius (d = 2r), which would give four times the base area times height; and πr^2 is just the area of the base, not accounting for height.