Which formula is used to find the volume and surface area of a right cone?

The formula used to find the volume and surface area of a right cone is found in option A, which consists of two parts: the volume and the surface area formulas.

The volume of a cone is given by the formula ( \frac{1}{3} \pi r^2 h ). This formula represents one-third of the area of the base (which is a circle, calculated as ( \pi r^2 )) multiplied by the height ( h ) of the cone. This relationship derives from the fact that a cone can be thought of as a pyramid with a circular base, and the one-third factor is a characteristic of pyramidal volumes.

For the surface area, the cone has two parts: the lateral surface area and the base area. The lateral surface area is calculated with the formula ( \pi r \sqrt{r^2 + h^2} ), where ( \sqrt{r^2 + h^2} ) represents the slant height of the cone. The base of the cone adds an additional area represented by ( \pi r^2 ). Thus, when these two components are combined, the total surface area formula becomes ( \pi r \sqrt{r^2 + h