Question

Height of the cylinder of maximum volume that can be inscribed in a sphere of radius 12 cm is

• A. $8\sqrt{3}$ cm
• B. $8$ cm
• C. $12\sqrt{3}$ cm
• D. $24$ cm

Answer 1

The correct option is A $8\sqrt{3}$ cm

$(\frac{h}{2}{)}^2+r^2=R^2$

Volume of cylinder $=\pi r^{2}h$

$=\pi (R^2-\frac{h^2}{4})h$

$\frac{dv}{dh}=\pi \left(\right(R^2-\frac{h^2}{4})-\frac{-2h^2}{4})$

$R^2=\frac{3h^2}{4}$

$\frac{2R}{\sqrt{3}}=h$

$h=8\sqrt{3}$