Question

The curved surface area of a cylinder is 1210 cm² and its diameter is 20 cm. Find its height and volume.

Answer 1

Curved surface area = 1210 cm²
Suppose that the height of cylinder is h cm.
We have r = 10 cm
$$\begin{gathered} \mathrm{Now},1210=2\mathrm{\pi }rh \\ \Rightarrow 1210=2\times \frac{22}{7}\times 10\times h\mathit{} \\ \Rightarrow h=\frac{1210\times 7}{2\times 22\times 10}=\frac{11\times 7}{2\times 2}=19.25\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}=\mathrm{\pi }{r}^{\mathit{2}}h\mathit{} \\ =\frac{22}{7}\times {10}^2\times 19.25{\mathrm{cm}}^3 \\ =2200\times 2.75{\mathrm{cm}}^3=6050{\mathrm{cm}}^3 \end{gathered}$$