Question

find the surface area of the cone below. leave your answer in terms of π. surface area of a cone sa = πrl + πr² (diagram shows cone with height 16 cm, radius 12 cm, slant height ℓ; sa = ?π cm²)

Explanation:

Step1: Find the slant height \( l \)

Using the Pythagorean theorem (\( l = \sqrt{r^2 + h^2} \)), where \( r = 12 \) cm and \( h = 16 \) cm.
\( l = \sqrt{12^2 + 16^2} = \sqrt{144 + 256} = \sqrt{400} = 20 \) cm.

Step2: Calculate the surface area

Use the formula \( SA = \pi rl + \pi r^2 \). Substitute \( r = 12 \), \( l = 20 \).
\( SA = \pi(12)(20) + \pi(12)^2 = 240\pi + 144\pi = 384\pi \).

Answer:

384