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

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

• A. (pi x r^2 x h)/3, pi x r x sqrt(r^2 + h^2) + pi x r^2
• B. pi x r^2 x h, 1/3(pi x r^2 h)
• C. (1/3)pi(r^3), 2(pi)r^2
• D. pi r^2 h, pi rh

Answer: (A)

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

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