Answer
$64\pi \text{ square inches}$
Work Step by Step
The variation model described by the problem is $
S=kr^2
,$ where $
S
$ is the surface area, and $
r
$ is the radius.
Substituting the known values in the variation model above results to
\begin{array}{l}\require{cancel}
36\pi=k(3)^2
\\
36\pi=k(9)
\\
\dfrac{36\pi}{9}=k
\\
k=4\pi
.\end{array}
Therefore, the variation equation is
\begin{array}{l}\require{cancel}
S=4\pi r^2
.\end{array}
Using the variation equation above, then
\begin{array}{l}\require{cancel}
S=4\pi (4)^2
\\
S=4\pi (16)
\\
S=64\pi
.\end{array}
Hence, the surface area, $S,$ is $
64\pi \text{ square inches}
.$
