A cap is cylindrical in shape, surmounted by a conical top. If the volume of the cylindrical part is

Question

A cap is cylindrical in shape, surmounted by a conical top. If the volume of the cylindrical part is equal to that of the conical part, then the ratio of the height of the cylindrical part to the height of the conical part is :\

Professor PC Thomas Classes · Answer

(b): Let height of cylindrical part $=h_{1}$; height of conical part $=h_{2}$ and radius of cylindrical part = radius of conical part = $r$\ Now, volume of cylindrical part\ = volume of conical part\ $\Rightarrow \pi r^{2} h_{1}=\frac{1}{3} \pi r^{2} h_{2}$\ $\Rightarrow \quad 3 h_{1}=h_{2}$\ $\Rightarrow \quad \frac{h_{1}}{h_{2}}=\frac{1}{3}$\  $\Rightarrow \quad h_{1}: h_{2}=1: 3$