• # question_answer A cone, a hemisphere and a cylinder stand on equal bases and have the same height what is the ratio of their volumes? A)  $2:1:3$                       B)  $2.5:1:3$     C)  $1:2:3$   D)  $1.5:2:3$

(c): As they stand on the same base so their radius is also same. Then; volume of cone $=\frac{\pi {{r}^{2}}h}{3}$ Volume of hemisphere $=\frac{2\pi {{r}^{3}}}{3}$;     Volume of cylinder $=\pi {{r}^{2}}h$ Ratio $=\frac{\pi {{r}^{2}}h}{3}:\frac{2\pi {{r}^{3}}}{3}:\pi {{r}^{2}}h$ $\Rightarrow$   $\frac{h}{3}:\frac{2r}{3}:h$ $\Rightarrow$   $h:2r:3h$      Radius of a hemisphere = It?s height So,      $h:2h:3h\Rightarrow 1:2:3$