Question

a solid consists of a circular cylinder surmounted by a right circular cone. the height of the cone is h. if the total height of the solid is 3 times the volume of the cone then the height of the cylinder is?? options: A) 2h B) 3h/2 C) h/2 D) 2h/3

Answer 1

$$\begin{gathered} \mathrm{Given} \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{cone}\mathrm{be}\mathrm{h} \\ \mathrm{Let}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{circular}\mathrm{cylinder}\mathrm{be}{\mathrm{h}}_1 \\ \mathrm{From}\mathrm{the}\mathrm{given}\mathrm{data} \\ \frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}+{\mathrm{\pi r}}^2{\mathrm{h}}_1=3\left(\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}\right) \\ \Rightarrow {\mathrm{\pi r}}^2\left(\frac{1}{3}\mathrm{h}+{\mathrm{h}}_1\right)={\mathrm{\pi r}}^2\mathrm{h} \\ \Rightarrow {\mathrm{h}}_1=\frac{2}{3}\mathrm{h} \end{gathered}$$