Which expression correctly gives the volume of a cone?

Prepare for the FBI Special Agent Selection System Phase I Test with comprehensive quizzes. Tackle flashcards and multiple-choice questions, complete with hints and explanations. Ace your exam!

Multiple Choice

Which expression correctly gives the volume of a cone?

Explanation:
The volume of a cone comes from applying the base area and the height, but because the cone tapers to a point, it only fills one third of the space that a cylinder with the same base and height would fill. The base is a circle with area π r^2, and the height is h, so the cone’s volume is V = (1/3) × (base area) × height = (1/3) π r^2 h. This matches the familiar idea that a cone is one third of a cylinder with the same base and height. The other expressions don’t fit: π r^2 h would be the cylinder’s volume, (4/3) π r^3 is the sphere’s volume, and π r h lacks the necessary r^2 factor to give a volume.

The volume of a cone comes from applying the base area and the height, but because the cone tapers to a point, it only fills one third of the space that a cylinder with the same base and height would fill. The base is a circle with area π r^2, and the height is h, so the cone’s volume is V = (1/3) × (base area) × height = (1/3) π r^2 h.

This matches the familiar idea that a cone is one third of a cylinder with the same base and height. The other expressions don’t fit: π r^2 h would be the cylinder’s volume, (4/3) π r^3 is the sphere’s volume, and π r h lacks the necessary r^2 factor to give a volume.

More practice questions