Question

A rectangular cardboard sheet of length 44 cm and breadth 15 cm is rolled along its length to form a cylinder find the curve surface area and the volume of this cylinder

Answer 1

$$\begin{gathered} \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{sheet}=44\mathrm{cm} \\ \mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{sheet}=15\mathrm{cm} \\ \mathrm{Now},\mathrm{when}\mathrm{the}\mathrm{rectangular}\mathrm{sheet}\mathrm{is}\mathrm{rolled}\mathrm{along}\mathrm{its}\mathrm{length},\mathrm{then}\mathrm{a}\mathrm{cylinder}\mathrm{is}\mathrm{formed}. \\ \mathrm{Now},\mathrm{circumference}\mathrm{of}\mathrm{base}=44\mathrm{cm} \\ \Rightarrow 2\mathrm{\pi r}=44 \\ \Rightarrow 2\times \frac{22}{7}\times \mathrm{r}=44\left(\mathrm{where},\mathrm{r}=\mathrm{radius}\right) \\ \Rightarrow \mathrm{r}=7\mathrm{cm} \\ \mathrm{Now},\mathrm{height}\mathrm{of}\mathrm{cylinder},\mathrm{h}=15\mathrm{cm} \\ \mathrm{CSA}=2\mathrm{\pi rh}=2\times \frac{22}{7}\times 7\times 15=660{\mathrm{cm}}^2 \\ \mathrm{Volume}={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times 7\times 7\times 15=2310{\mathrm{cm}}^3 \end{gathered}$$