Answer
$9 \pi \;m^2$
Work Step by Step
The given values are
Height $h=5\;m$.
Volume $V=15 \pi \;m^3$.
Let the radius of the base is $r$.
Formula:-
Base area $B=\pi r^2$.
Volume $V= \frac{1}{3}\pi r^2 h$.
Substitute $\pi r^2=B$.
$\Rightarrow V= \frac{1}{3}B h$.
Substitute $V=15 \pi \;m^3$ and $h=5\;m$.
$\Rightarrow 15 \pi \;m^3= \frac{1}{3}B (5\;m)$.
Multiply both sides by $\frac{3}{5\;m}$.
$\Rightarrow \frac{3}{5\;m}\cdot 15 \pi \;m^3= \frac{3}{5\;m}\cdot \frac{1}{3}B (5\;m)$.
Simplify.
$\Rightarrow 9 \pi \;m^2= B $.
Hence the base area $9 \pi \;m^2$.
