Question

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their curved surface areas.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{radii}\mathrm{of}\mathrm{two}\mathrm{cylinders}\mathrm{be}2r\mathrm{and}3r,\mathrm{respectively},\mathrm{and}\mathrm{their}\mathrm{heights}be5h\mathrm{and}3h,\mathrm{respectively}. \\ \mathrm{Let}{\mathrm{S}}_1\mathrm{and}{\mathrm{S}}_2\mathrm{be}\mathrm{the}\mathrm{curved}\mathrm{surface}\mathrm{areas}\mathrm{of}\mathrm{the}\mathrm{two}\mathrm{cylinder}. \\ {\mathrm{S}}_1=Curved\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cylinder}\mathrm{of}\mathrm{height}5h\mathrm{and}\mathrm{radius}2r \\ {\mathrm{S}}_2=Curved\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cylinder}\mathrm{of}\mathrm{height}3h\mathrm{and}\mathrm{radius}3r \\ \therefore {\mathrm{S}}_1:{\mathrm{S}}_2=2\times \mathrm{\pi }\times r\times h:2\times \mathrm{\pi }\times r\times h \\ =\frac{2\times \mathrm{\pi }\times 2r\times 5h}{2\times \mathrm{\pi }\times 3r\times 3h} \\ =10:9 \end{gathered}$$