Question

the circumference of the base of a cone is 24π inches. the slant height of the cone is 20. 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 base radius

Given circumference $C=24\pi$, use $C=2\pi r$.
$\displaystyle r=\frac{C}{2\pi}=\frac{24\pi}{2\pi}=12$ inches

Step2: Calculate base area

Use circle area formula $A_b=\pi r^2$.
$\displaystyle A_b=\pi (12)^2=144\pi$ square inches

Step3: Calculate lateral surface area

Use formula $A_l=\pi r l$, where $l=20$.
$\displaystyle A_l=\pi \times 12 \times 20=240\pi$ square inches

Step4: Total surface area

Sum base and lateral areas.
$\displaystyle A_{total}=144\pi + 240\pi=384\pi$ square inches

Answer:

384π square inches