Question

) A sphere and a right circular cylinder have the same radius. If the volume of the sphere is f ive times the volume of the cylinder, then what is the ratio of cylinder's height and radius

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{sphere}\mathrm{and}\mathrm{cylinder}\mathrm{be}\mathrm{r}\mathrm{units}. \\ \mathrm{And}\mathrm{height}\mathrm{of}\mathrm{cylinder}\mathrm{be}\mathrm{h}\mathrm{units}. \\ \mathrm{According}\mathrm{to}\mathrm{question}, \\ \mathrm{Volume}\mathrm{of}\mathrm{sphere}=5\times \mathrm{Volume}\mathrm{of}\mathrm{cylinder} \\ \Rightarrow \frac{4}{3}{\mathrm{\pi r}}^3=5\times {\mathrm{\pi r}}^2\mathrm{h} \\ \Rightarrow \frac{\mathrm{r}}{\mathrm{h}}=\frac{15}{4} \\ \Rightarrow \frac{\mathrm{h}}{\mathrm{r}}=\frac{4}{15} \\ \mathrm{So},\mathrm{the}\mathrm{required}\mathrm{ratio}\mathrm{is}4:15 \end{gathered}$$
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