SSC CGL Model Paper 1

For max. volume AB = BC
Applying Pythagoras
$\mathit{A}{\mathit{B}}^2+\mathit{B}{\mathit{C}}^2={\left(20\right)}^2$ $\Rightarrow \mathit{A}\mathit{B}=\mathit{B}\mathit{C}=10\sqrt{2}$
Figure is rotated along AC, a double cone will form with radius BD
In $\mathrm{\Delta }\mathrm{ABC};\mathit{A}\mathit{B}\times \mathit{B}\mathit{C}=\mathit{B}\mathit{D}\times \mathit{A}\mathit{C}$
$10\sqrt{2}\times 10\sqrt{2}=\mathit{B}\mathit{D}\times 20$
BD = 10
Hence, Volume of cone of radius 10cm and height 10 cm is given by $=\frac{1}{3}\mathit{\pi }{\mathit{r}}^2\mathit{h}$
$=\frac{1}{3}\mathit{\pi }\times 100\times 10=1000\frac{\mathit{\pi }}{3}$
Volume of required double cone $=2\times 1000\frac{\mathit{\pi }}{3}$
$=\frac{2000}{3}\mathit{\pi }$