Question

find the surface area of the cone below. leave your answer in terms of π.
surface area
of a cone
sa = πrl + πr²
diagram of cone with height 4 cm, radius 3 cm
sa = ?π cm²

Explanation:

Step1: Find the slant height \( l \)

Using the Pythagorean theorem (\( l = \sqrt{r^2 + h^2} \)), where \( r = 3 \) cm and \( h = 4 \) cm.
\( l = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \) cm.

Step2: Calculate the surface area

Use the formula \( SA = \pi rl + \pi r^2 \). Substitute \( r = 3 \) and \( l = 5 \).
\( SA = \pi(3)(5) + \pi(3)^2 = 15\pi + 9\pi = 24\pi \).

Answer:

24