Question

the lateral surface area, s, of a cone is the product of pi, the radius, and the slant height. the formula below calculates the lateral surface area of a cone with a radius of 15 units.

s = 15π(15² + h²)½

which of the following describes (15² + h²)½?

a. the measure of the diameter of the cone

b. the measure of the area of the base of the cone

c. the measure of the slant height of the cone

Explanation:

In a right - triangle formed by the radius \(r = 15\), height \(h\) and slant height \(l\) of a cone, by the Pythagorean theorem \(l=\sqrt{r^{2}+h^{2}}\). Here \(r = 15\), so \(l=(15^{2}+h^{2})^{\frac{1}{2}}\) (since \(\sqrt{x}=x^{\frac{1}{2}}\)).

Answer:

C. the measure of the slant height of the cone