What is the volume formula for a cone?

What is the volume formula for a cone?

• A. 1/3 × π × r² × h
• B. π × r² × h
• C. 1/2 × base area × height
• D. 2 × π × r × h

Answer: (A)

The volume formula for a cone is given by the expression \( \frac{1}{3} \times \pi \times r^2 \times h \). This formula is derived from the general principles of geometry, specifically the relationship between the volume of a cone and that of a cylinder. A cone can be thought of as a pyramid with a circular base. The formula reflects that the volume of the cone is one-third of the volume of a cylinder that has the same base area (which is \( \pi r^2 \)) and height \( h \). The factor of one-third accounts for the geometric property that a cone fills one-third of the bounding cylinder's space. In summary, this formula accurately represents how the dimensions (the radius of the base and the height) contribute to the total volume of a cone, making it a central formula in geometry related to three-dimensional shapes.

The volume formula for a cone is given by the expression ( \frac{1}{3} \times \pi \times r^2 \times h ). This formula is derived from the general principles of geometry, specifically the relationship between the volume of a cone and that of a cylinder.

A cone can be thought of as a pyramid with a circular base. The formula reflects that the volume of the cone is one-third of the volume of a cylinder that has the same base area (which is ( \pi r^2 )) and height ( h ). The factor of one-third accounts for the geometric property that a cone fills one-third of the bounding cylinder's space.

In summary, this formula accurately represents how the dimensions (the radius of the base and the height) contribute to the total volume of a cone, making it a central formula in geometry related to three-dimensional shapes.