Question

find the surface area of the cone below. leave your answer in terms of π. surface area of a cone sa = πrℓ + πr² sa = ?π cm²

Explanation:

Step1: Find the slant height $\ell$

Use the Pythagorean theorem $\ell=\sqrt{24^{2}+18^{2}}=\sqrt{576 + 324}=\sqrt{900}=30$ cm.

Step2: Calculate the surface - area

The formula for the surface area of a cone is $SA=\pi r\ell+\pi r^{2}$. Substitute $r = 18$ cm and $\ell=30$ cm.
$SA=\pi\times18\times30+\pi\times18^{2}=540\pi+324\pi$.
$SA = 864\pi$ $cm^{2}$.

Answer:

$864\pi$