Question

if volume and the base area of a right circular cone are 48π cm^3 12π cm^3 then find the height of the cone .

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{r}\mathrm{be}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{base}\mathrm{and}\mathrm{h}\mathrm{be}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{cone}. \\ \mathrm{volume}\mathrm{of}\mathrm{cone}=48\mathrm{\pi }{\mathrm{cm}}^3 \\ \Rightarrow \frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=48\mathrm{\pi }...\left(1\right) \\ \mathrm{area}\mathrm{of}\mathrm{base}\mathrm{of}\mathrm{cone}=12\mathrm{\pi }{\mathrm{cm}}^2 \\ \Rightarrow {\mathrm{\pi r}}^2=12\mathrm{\pi }...\left(2\right) \\ \mathrm{Now},\mathrm{from}\left(1\right), \\ \frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=48\mathrm{\pi } \\ \Rightarrow \frac{1}{3}\times 12\mathrm{\pi }\times \mathrm{h}=48\mathrm{\pi }\left[\mathrm{using}\left(2\right)\right] \\ \Rightarrow 4\mathrm{h}=48 \\ \Rightarrow \mathrm{h}=12\mathrm{cm} \end{gathered}$$