Question

find the surface area of the cone below. leave your answer in terms of π.
diagram of a cone with height 24 cm, radius 18 cm, slant height ( ell ), and a yellow box with: surface area of a cone ( sa = pi rell + pi r^2 )
( sa = \boxed{?} pi , \text{cm}^2 )

Explanation:

Step1: Find the slant height \( \ell \)

Using the Pythagorean theorem (\( \ell = \sqrt{r^2 + h^2} \)), where \( r = 18 \) cm and \( h = 24 \) cm.
\( \ell = \sqrt{18^2 + 24^2} = \sqrt{324 + 576} = \sqrt{900} = 30 \) cm.

Step2: Calculate the surface area

Use the formula \( SA = \pi r\ell + \pi r^2 \). Substitute \( r = 18 \), \( \ell = 30 \):
\( SA = \pi(18)(30) + \pi(18)^2 = 540\pi + 324\pi = 864\pi \).

Answer:

\( 864 \)