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 \( l \)

Use the Pythagorean theorem \( l=\sqrt{r^{2}+h^{2}} \). Given \( r = 18\) cm and \( h=24\) cm.

$$ l=\sqrt{18^{2}+24^{2}}=\sqrt{324 + 576}=\sqrt{900}=30\text{ cm} $$

Step2: Calculate the surface area \( SA \)

Use the formula \( SA=\pi rl+\pi r^{2}\). Substitute \( r = 18\) cm and \( l = 30\) cm.

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Answer:

\(864\pi\)