Question

The curved surface area of a cylinder is 1320 cm square and its base has diameter 21 cm. Find the height and volume of the cylinder.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{r}\mathrm{be}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{base}\mathrm{and}\mathrm{h}\mathrm{be}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cylinder}. \\ \mathrm{Now},\mathrm{diameter}\mathrm{of}\mathrm{base}=21\mathrm{cm} \\ \mathrm{so},\mathrm{r}=\frac{\mathrm{diameter}\mathrm{of}\mathrm{base}}{2}=\frac{21}{2}\mathrm{cm} \\ \mathrm{Now},\mathrm{CSA}=1320{\mathrm{cm}}^2 \\ \Rightarrow 2\mathrm{\pi rh}=1320 \\ \Rightarrow 2\times \frac{22}{7}\times \frac{21}{2}\times \mathrm{h}=1320 \\ \Rightarrow \mathrm{h}=20\mathrm{cm} \\ \mathrm{Now},\mathrm{Volume}={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times \frac{21}{2}\times \frac{21}{2}\times 20=6930{\mathrm{cm}}^3 \end{gathered}$$