Which expression represents the volume of a right circular cone with radius r and height h?

• A. 1/3 pi r h^2
• B. 1/3 h^3 pi
• C. 1/3 pi r^3
• D. 1/3 pi r^2 h

Answer: (D)

The volume of a cone equals one-third of the base area times the height. For a right circular cone, the base is a circle with area pi r^2, so the volume is (1/3) times pi r^2 times h, written as (1/3) pi r^2 h. This shows why the expression with r^2 and h is the correct form: it uses the base area pi r^2 and multiplies by the height, then scales by 1/3 to account for the cone’s tapering. The other options mix in r^3 or h^3 or omit the r^2 term, which doesn’t reflect the circular base area.