Question

find the surface area of the cone below. leave your answer in terms of \\(\pi\\). surface area of a cone \\(sa = \pi r\ell + \pi r^2\\) \\(sa = ?\pi\\,\text{cm}^2\\)

Explanation:

Step1: Find the slant height \( l \)

Using the Pythagorean theorem in the right triangle (height \( h = 12 \) cm, radius \( r = 9 \) cm, slant height \( l \)):
\( l=\sqrt{r^{2}+h^{2}}=\sqrt{9^{2}+12^{2}}=\sqrt{81 + 144}=\sqrt{225}=15 \) cm.

Step2: Calculate the surface area

The formula for the surface area of a cone is \( SA=\pi rl+\pi r^{2} \). Substitute \( r = 9 \), \( l = 15 \):
\( SA=\pi(9)(15)+\pi(9)^{2}=135\pi + 81\pi=216\pi \).

Answer:

\( 216 \)