Question

the radii of cylinders are in ratio 3:2 and their heights are in ratio 4:5 calculate the ratio of their curved surface area

Answer 1

$$\begin{gathered} \mathrm{Let}{\mathrm{r}}_1\mathrm{and}{\mathrm{r}}_2\mathrm{be}\mathrm{the}\mathrm{radii}\mathrm{of}\mathrm{two}\mathrm{cylinders}\mathrm{and}{\mathrm{h}}_1\mathrm{and}{\mathrm{h}}_2\mathrm{be}\mathrm{their}\mathrm{heights}. \\ \mathrm{Now},\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\frac{3}{2}\mathrm{and}\frac{{\mathrm{h}}_1}{{\mathrm{h}}_2}=\frac{4}{5} \\ \mathrm{Now},\frac{\mathrm{CSA}\mathrm{of}\mathrm{first}\mathrm{cylinder}}{\mathrm{CSA}\mathrm{of}\mathrm{second}\mathrm{cylinder}}=\frac{2{\mathrm{\pi r}}_1{\mathrm{h}}_1}{2{\mathrm{\pi r}}_2{\mathrm{h}}_2} \\ \Rightarrow \frac{\mathrm{CSA}\mathrm{of}\mathrm{first}\mathrm{cylinder}}{\mathrm{CSA}\mathrm{of}\mathrm{second}\mathrm{cylinder}}=\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}\times \frac{{\mathrm{h}}_1}{{\mathrm{h}}_2}=\frac{3}{2}\times \frac{4}{5}=\frac{6}{5} \\ \Rightarrow \mathrm{CSA}\mathrm{of}\mathrm{first}\mathrm{cylinder}:\mathrm{CSA}\mathrm{of}\mathrm{second}\mathrm{cylinder}=6:5 \end{gathered}$$