The volume of a right circular cone with radius r and height h is which expression?

• A. v = (1/3) π r^2 h
• B. v = π r^2 h
• C. v = π r h^2
• D. v = π r^3

Answer: (A)

The volume is found by taking the base area and the height, but for a cone only a third of the corresponding cylinder’s volume is filled. The base area is πr^2, so the cylinder with the same base and height has volume πr^2h. Since the cone is one-third of that, the volume is V = (1/3)πr^2h. This matches the dimensions of volume and aligns with how a cone’s cross-sections scale with height. The other expressions would describe a cylinder (πr^2h), a form that mixes radius and height in a nonmatching way (πrh^2), or a radius-only term (πr^3), none of which correctly represent the cone’s volume.