Question

A cone and a sphere have the same height and equal radii. what is the ratio of their volumes?

Answer 1

Dear student
$$\begin{gathered} Given:coneandspherehasequalheightandequalradii. \\ Volumeofcone=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h} \\ \mathrm{Volume}\mathrm{of}\mathrm{sphere}=\frac{4}{3}{\mathrm{\pi r}}^3 \\ \mathrm{So},\frac{\mathrm{Volume}\mathrm{of}\mathrm{cone}}{\mathrm{Volume}\mathrm{of}\mathrm{sphere}}=\frac{\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}}{\frac{4}{3}{\mathrm{\pi r}}^3}=\frac{\mathrm{h}}{4\mathrm{r}}=\frac{\mathrm{r}}{4\mathrm{r}}=1:4\left(\mathrm{As}\mathrm{h}=\mathrm{r}\right) \end{gathered}$$
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