Question

find the surface area of the cone below. leave your answer in terms of π. surface area of a cone ( sa=pi rell+pi r^{2} ) ( sa=?pi cm^{2} )

Explanation:

Step1: Find the slant height

Using 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 \(r = 3\) cm and \(l = 5\) cm.
\(SA=\pi\times3\times5+\pi\times3^{2}=15\pi+9\pi\)

Step3: Simplify the expression

\(15\pi+9\pi=(15 + 9)\pi=24\pi\)

Answer:

\(24\pi\)