Question

the volume and curved surface area of a cylinder are 1650 cm cube and 660 cm square respectively.find the radius and height of the cylinder

Answer 1

Here is the solution:
$$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{cylinder}=1650{\mathrm{cm}}^3 \\ {\mathrm{\pi r}}^2\mathrm{h}=1650{\mathrm{cm}}^3...\left(\mathrm{i}\right) \\ \mathrm{Curved}\mathrm{surface}\mathrm{area}=660{\mathrm{cm}}^2 \\ 2\mathrm{\pi rh}=660{\mathrm{cm}}^3...\left(\mathrm{ii}\right) \\ \frac{{\mathrm{\pi r}}^2\mathrm{h}}{2\mathrm{\pi rh}}=\frac{1650}{660} \\ \Rightarrow \mathrm{r}=5\mathrm{cm} \\ \mathrm{Put}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{r}\mathrm{in}\mathrm{equation}\left(\mathrm{i}\right) \\ \frac{22}{7}\times 5^2\times \mathrm{h}=1650 \\ \Rightarrow \mathrm{h}=\frac{1650\times 7}{22\times 25}=21\mathrm{cm} \end{gathered}$$