Question

find the surface area of the cone below. leave your answer in terms of π. surface area of a cone sa = πrl + πr²

Explanation:

Step1: Find the slant height \( l \)

Using the Pythagorean theorem (\( l = \sqrt{r^2 + h^2} \)), where \( r = 9 \) cm and \( h = 12 \) cm.
\( l = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15 \) cm.

Step2: Calculate the surface area

Use the formula \( SA = \pi r l + \pi r^2 \). Substitute \( r = 9 \) and \( l = 15 \).
\( SA = \pi(9)(15) + \pi(9)^2 = 135\pi + 81\pi = 216\pi \).

Answer:

216