Mathematics - Application of Derivative Question with Solution | TestHub

From the diagram, we get radius of cylinder$=\sqrt{R^2-{\left(\frac{h}{2}\right)}^2}$
$\Rightarrow$Volume of cylinder$V=\pi \left(R^2-\frac{h^2}{4}\right)h$
For maximum volume:$\frac{dV}{dh}=0$
$\Rightarrow \pi \left(R^2-\frac{{3h}^2}{4}\right)=0$
$\Rightarrow h^2=\frac{4R^2}{3}=\frac{4\times 9}{3}=12$
$\Rightarrow h=2\sqrt{3}$