What is the formula for the volume of a cone?

• A. V = 1/3πr^2h
• B. V = πr^2h
• C. V = 3πr^2h
• D. V = πr^3h

Answer: (A)

This question tests how the cone’s volume relates to a cylinder with the same base and height. The cone’s volume is one-third of that cylinder’s volume, because the cross-sectional area in a cone shrinks linearly from the base to the tip, so it occupies only a third of the space inside the same-height cylinder.

From this, the volume formula becomes V = (1/3) × base area × height. The base area is πr^2, so V = (1/3) π r^2 h.

The other forms would either give the cylinder’s volume (no one-third factor), triple the cone’s volume, or use r^3 which doesn’t match how the base scales with radius.