Question

a rectangular sheet of paper of dimensions 44cm*22cm is rolled first along its length and then along its breadth to form a cylinder. find the ratio of the crved surface areas of the two cylinders thus formed.

Answer 1

Dear Student,

$$\begin{gathered} L=44cm,B=22cm \\ Rolledalongitslength, \\ Circumference=Length=2\mathrm{\pi R} \\ \mathrm{R}=\frac{44}{2\mathrm{\pi }}=7\mathrm{cm} \\ \mathrm{Height}=\mathrm{Breadth}=22\mathrm{cm} \\ \mathrm{CSA}=2\mathrm{\pi RH}=2\mathrm{\pi }\times 7\times 22=308\mathrm{\pi }{\mathrm{cm}}^2 \\ \mathrm{Rolled}\mathrm{along}\mathrm{its}\mathrm{breadth}, \\ \mathrm{Circumference}=\mathrm{Breadth}=2\mathrm{\pi R} \\ \mathrm{R}=\frac{22}{2\mathrm{\pi }}=3.5\mathrm{cm} \\ \mathrm{Height}=\mathrm{Length}=44\mathrm{cm} \\ \mathrm{CSA}=2\mathrm{\pi RH}=2\mathrm{\pi }\times 3.5\times 44=308\mathrm{\pi }{\mathrm{cm}}^2 \\ \mathrm{Ratio}\mathrm{of}\mathrm{the}\mathrm{two}\mathrm{is}1:1 \end{gathered}$$

Regards