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: Substitute the values into the formula

The formula for the surface area of a cone is \(SA=\pi rl+\pi r^{2}\). Given \(r = 9\) cm and \(l=21\) cm.
Substitute \(r = 9\) and \(l = 21\) into \(SA=\pi rl+\pi r^{2}\), we get \(SA=\pi\times9\times21+\pi\times9^{2}\).

Step2: Calculate each term

First term: \(\pi\times9\times21 = 189\pi\).
Second term: \(\pi\times9^{2}=\pi\times81 = 81\pi\).

Step3: Add the two terms

\(SA=189\pi + 81\pi=(189 + 81)\pi\).
Since \(189+81=270\), so \(SA = 270\pi\).

Answer:

\(270\pi\)