• # question_answer A cone is inscribed in a hemisphere such that their bases are common. If C is the volume of the cone and H that of the hemisphere, then what is the value of$C:H$? A)  $1:2$           B)         $2:3$             C)         $3:4$             D)         $4:5$

Volume of cone, $C=\frac{1}{3}\pi \,{{R}^{2}}H$             $=\frac{1}{3}\pi {{R}^{3}}$                    $(\because \,H=R)$ Volume of hemisphere, $H=\frac{2}{3}\pi {{R}^{3}}$ $\therefore$     $C:H=\frac{1}{3}\pi {{R}^{3}}:\frac{2}{3}\pi {{R}^{3}}=1:2$