Question

Savia had to make a model of a cylindrical kaleidoscope for her science project. She used a chart paper of dimensions 44cm x 25cm and rolled it along its greater side in such a way that the side AD coincides with side BC. Find the radius and height of the model so formed.

Answer 1

$$\begin{gathered} \mathrm{As}\mathrm{the}\mathrm{chart}\mathrm{paper}\mathrm{is}\mathrm{rolled}\mathrm{along}\mathrm{its}\mathrm{length},\mathrm{the}\mathrm{width}\mathrm{of}\mathrm{the}\mathrm{paper} \\ \mathrm{becomes}\mathrm{the}\mathrm{circumference}\mathrm{of}\mathrm{the}\mathrm{base}\mathrm{of}\mathrm{the}\mathrm{cylinder}. \\ \mathrm{i},\mathrm{e} \\ 2\mathrm{\pi r}=25 \\ \Rightarrow \mathrm{r}=\frac{25}{2\mathrm{\pi }}=3.97\mathrm{cm} \\ \mathrm{Height}\mathrm{will}\mathrm{be}\mathrm{equal}\mathrm{to}\mathrm{length}\mathrm{of}\mathrm{paper} \\ \mathrm{Thus}\mathrm{height}=44\mathrm{cm} \end{gathered}$$