Question

The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 m², find the circumference of its base.

Answer 1

$$\begin{gathered} \mathrm{Let}r\mathrm{and}h\mathrm{be}\mathrm{the}\mathrm{radius}\mathrm{and}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{cylinder}. \\ \mathrm{Given}: \\ r+h=37\mathrm{m} \\ \mathrm{Total}\mathrm{surface}\mathrm{area},S=2\mathrm{\pi }r\left(r+h\right) \\ 1628=2\mathrm{\pi }\times r\times 37 \\ \mathrm{r}=\frac{1628}{2\mathrm{\pi }\times 37} \\ =\frac{1628}{232.477} \\ =7\mathrm{m} \\ \mathrm{Circumference}\mathrm{of}\mathrm{its}\mathrm{base},S_{\mathit{1}}=2\mathrm{\pi r} \\ =\left(2\times \frac{22}{7}\times 7\right)\mathrm{m} \\ =44\mathrm{m} \end{gathered}$$