Question

A rectangular sheet of paper, 44 cm × 20 cm, is rolled along its length to form a cylinder. Find the volume of the cylinder so formed.

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{length}\left(l\right)\mathrm{and}\mathrm{breadth}\left(b\right)\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{sheet}\mathrm{are}44\mathrm{cm}\mathrm{and}20\mathrm{cm} \\ \mathrm{Now},\mathrm{the}\mathrm{sheet}\mathrm{is}\mathrm{rolled}\mathrm{along}\mathrm{the}\mathrm{length}\mathrm{to}\mathrm{form}\mathrm{a}\mathrm{cylinder}. \\ \mathrm{Let}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{cylinder}\mathrm{be}r\mathrm{cm}. \\ \mathrm{Height},h=b=20\mathrm{cm} \\ \mathrm{Circumference},S=44\mathrm{cm} \\ 2\mathrm{\pi }r=44\mathrm{cm} \\ 2\times \frac{22}{7}\times r=44\mathrm{cm} \\ r=7\mathrm{cm} \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder},\mathrm{V}=\mathrm{\pi }{r}^{2}h \\ =\frac{22}{7}\times 7^2\times 20{\mathrm{cm}}^3 \\ =3080{\mathrm{cm}}^3 \end{gathered}$$