Question

The sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq metres, then find its volume.

Answer 1

Let r and h be the base radius and the height of the solid cylinder, respectively.

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ (r+h)=37\mathrm{m} \\ \mathrm{As},\mathrm{the}\mathrm{total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cylinder}=1628{\mathrm{m}}^2 \\ \Rightarrow 2\mathrm{\pi }r\left(r+h\right)=1628 \\ \Rightarrow 2\times \frac{22}{7}\times r\times 37=1628 \\ \Rightarrow r=\frac{1628\times 7}{2\times 22\times 37} \\ \Rightarrow r=7\mathrm{m} \\ \mathrm{So},h=\left(37-7\right)=30\mathrm{m} \end{gathered}$$

$$\begin{gathered} \mathrm{Now},\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{cylinder}=\mathrm{\pi }{r}^{2}h \\ =\frac{22}{7}\times 7\times 7\times 30 \\ =4620{\mathrm{m}}^3 \end{gathered}$$