#### Answer

$\text{approximately } 62.8 \text{ centimeters}$

#### Work Step by Step

Substituting $h=3$ and $r=4$ in the given equation, $
A=\pi r\sqrt{r^2+h^2}
,$ results to
\begin{array}{l}\require{cancel}
A=\pi (4)\sqrt{4^2+3^2}
\\
A=4\pi\sqrt{16+9}
\\
A=4\pi\sqrt{25}
\\
A=4\pi\sqrt{(5)^2}
\\
A=4\pi(5)
\\
A=20\pi
\\
A\approx62.8
.\end{array}
Hence, the lateral surface area, $A,$ is $
\text{approximately } 62.8 \text{ centimeters}
.$