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\space cm^2\\)

Explanation:

Step1: Find the slant height \( l \)

Using the Pythagorean theorem in the right triangle (height \( h = 24 \) cm, radius \( r = 18 \) cm, slant height \( l \)):
\( l=\sqrt{r^{2}+h^{2}}=\sqrt{18^{2}+24^{2}} \)
\( 18^{2}=324 \), \( 24^{2}=576 \), so \( l=\sqrt{324 + 576}=\sqrt{900}=30 \) cm.

Step2: Calculate \( \pi rl \)

Substitute \( r = 18 \), \( l = 30 \):
\( \pi rl=\pi\times18\times30 = 540\pi \)

Step3: Calculate \( \pi r^{2} \)

Substitute \( r = 18 \):
\( \pi r^{2}=\pi\times18^{2}=\pi\times324 = 324\pi \)

Step4: Sum the two terms for surface area

\( SA=\pi rl+\pi r^{2}=540\pi + 324\pi = 864\pi \)

Answer:

\( 864 \)