Question

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

Answer 1

We have r + h = 37, where r m is the radius and h m is the height of the given cylinder.
i.e., h = 37 − r
Total surface area = 1628 m²
$$\begin{gathered} \Rightarrow 2\mathrm{\pi }rh+2\mathrm{\pi }{r}^2=1628 \\ \Rightarrow 2\times \frac{22}{7}\left[r\left(37-r\right)+r^2\right]=1628 \\ \Rightarrow 37r-r^{\mathit{2}}\mathit{+}{r}^2=\frac{1628\times 7}{44} \\ \Rightarrow 37r=37\times 7 \\ \Rightarrow r=7\mathrm{m} \end{gathered}$$

Then h = 37 − 7 = 30 m

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