What is the formula for the volume of a cone?

What is the formula for the volume of a cone?

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

Answer: (B)

The volume of a cone is one third of the volume of a cylinder that has the same base and height. The base is a circle with area πr^2, so the cylinder with the same base and height has volume πr^2h. Since the cone fills only a third of that space, its volume is V = (1/3)πr^2h. This uses the circle’s base area and the height, with the correct one-third factor to account for how a cone fits into the cylinder. The other forms miss either the squared radius in the base area, the one-third factor, or scale the volume incorrectly, so they don’t match the cone’s actual volume.

The volume of a cone is one third of the volume of a cylinder that has the same base and height. The base is a circle with area πr^2, so the cylinder with the same base and height has volume πr^2h. Since the cone fills only a third of that space, its volume is V = (1/3)πr^2h. This uses the circle’s base area and the height, with the correct one-third factor to account for how a cone fits into the cylinder. The other forms miss either the squared radius in the base area, the one-third factor, or scale the volume incorrectly, so they don’t match the cone’s actual volume.