Question

the radii of two cylinders are in the ratio 3:5andtheir height are in the ratio 2:3 find the ratio of their curved surface area?

Answer 1

$$\begin{gathered} \mathrm{Let}{\mathrm{r}}_1\mathrm{and}{\mathrm{h}}_1\mathrm{be}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{base}\mathrm{and}\mathrm{height}\mathrm{of}\mathrm{first}\mathrm{cylinder}. \\ \mathrm{Let}{\mathrm{r}}_2\mathrm{and}{\mathrm{h}}_2\mathrm{be}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{base}\mathrm{and}\mathrm{height}\mathrm{of}\mathrm{second}\mathrm{cylinder}. \\ \mathrm{Now},\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\frac{3}{5}\mathrm{and}\frac{{\mathrm{h}}_1}{{\mathrm{h}}_2}=\frac{2}{3} \\ \mathrm{Now},\frac{\mathrm{CSA}\mathrm{of}\mathrm{first}\mathrm{cylinder}}{\mathrm{CSA}\mathrm{of}\mathrm{second}\mathrm{cylinder}}=\frac{2{\mathrm{\pi r}}_1{\mathrm{h}}_1}{2{\mathrm{\pi r}}_2{\mathrm{h}}_2}=\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}\times \frac{{\mathrm{h}}_1}{{\mathrm{h}}_2}=\frac{3}{5}\times \frac{2}{3}=\frac{2}{5} \end{gathered}$$