What is the formula for the volume of a cone with base radius r and height h?

What is the formula for the volume of a cone with base radius r and height h?

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

Answer: (A)

The main idea is that the volume of a cone is one third of the volume of a cylinder that shares the same base and height. The base area is π r^2, so the cylinder's volume would be π r^2 h. A cone is one third of that, giving V = (1/3) π r^2 h. This matches the general rule for pyramids: volume equals base area times height, divided by 3. The other options either describe the cylinder’s volume, or mix in the height incorrectly or use an incorrect constant, so they don’t fit the geometric relationship.

The main idea is that the volume of a cone is one third of the volume of a cylinder that shares the same base and height. The base area is π r^2, so the cylinder's volume would be π r^2 h. A cone is one third of that, giving V = (1/3) π r^2 h. This matches the general rule for pyramids: volume equals base area times height, divided by 3. The other options either describe the cylinder’s volume, or mix in the height incorrectly or use an incorrect constant, so they don’t fit the geometric relationship.