Question

The lateral surface area of a cylinder is 2816 sq cm.it is cut along its height and formed a rectangular sheet of length 44cm.find the radius and height of the cylinder.

Answer 1

$$\begin{gathered} \mathrm{Hi}, \\ \mathrm{cut}\mathrm{is}\mathrm{made}\mathrm{along}\mathrm{height}\mathrm{so}\mathrm{width}\mathrm{of}\mathrm{the}\mathrm{sheet}\mathrm{will}\mathrm{be}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{cylinder} \\ \mathrm{so}\mathrm{here}\mathrm{length}\mathrm{of}\mathrm{rectangle}=44\mathrm{cm} \\ \mathrm{and}\mathrm{lateral}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{cylinder}=\mathrm{area}\mathrm{of}\mathrm{sheet}\left(\mathrm{rectangular}\right) \\ 2816=44\times \mathrm{width} \\ \mathrm{width}=\frac{2816}{44}=64\mathrm{cm}=\mathrm{height}\mathrm{of}\mathrm{cylinder} \\ \mathrm{so}\mathrm{using},2\mathrm{\pi rh}=2816 \\ 2\times \frac{22}{7}\times \mathrm{r}\times 64=2816 \\ \mathrm{r}=\frac{2816\times 7}{44\times 64}=7\mathrm{cm} \end{gathered}$$