Question

the circumference of the base of a cone is 24π inches. the slant height of the cone is 20 inches. what is the surface area of the cone? express the answer in terms of π. 240π square inches 384π square inches 480π square inches 624π square inches

Explanation:

Step1: Find the radius of the base

The formula for the circumference of a circle is $C = 2\pi r$. Given $C=24\pi$, we have $2\pi r=24\pi$. Solving for $r$, we divide both sides by $2\pi$: $r=\frac{24\pi}{2\pi}=12$ inches.

Step2: Calculate the surface - area of the cone

The formula for the surface area of a cone is $S=\pi rl+\pi r^{2}$, where $l$ is the slant height and $r$ is the radius. We know $r = 12$ inches and $l = 20$ inches. First, calculate $\pi rl=\pi\times12\times20 = 240\pi$. Second, calculate $\pi r^{2}=\pi\times12^{2}=144\pi$. Then $S=240\pi + 144\pi=384\pi$ square inches.

Answer:

B. 384π square inches