Question

A right circular cylinder with radius $r$ and height $h$ has the surface area $S$ (in square units) given by the formula $S=2 \pi r(r+h) .$  Find the surface area of a cylinder with radius 6 in. and height 9 in. Leave the answer in terms of $\pi$.

Answer 1

Evaluate the expression $2 \pi r(r+h)$ for $r=6$ and $h=9$.
$$
\begin{aligned}
S &=2 \pi r(r+h) \\
&=2 \pi(6)[(6)+(9)] \\
&=2 \pi(6)(15) \\
&=180 \pi
\end{aligned}
$$
The surface area is $180 \pi$ square inches.