Question

The curved surface area of a cylinder is 4400 cm² and the circumference of the base is 110 cm. Find the volume of the cylinder.

Answer 1

$$\begin{gathered} \mathrm{Circumference}\mathrm{of}\mathrm{base}\mathrm{of}\mathrm{cylinder}=110\mathrm{cm} \\ \Rightarrow 2\mathrm{\pi }r=110 \\ \Rightarrow 2\times \frac{22}{7}\times r=110 \\ \Rightarrow r=\frac{110\times 7}{44}=17.5\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{cylinder}=4400{\mathrm{cm}}^2 \\ \Rightarrow 2\mathrm{\pi }rh\mathit{}=4400 \\ \Rightarrow h\mathit{}=\frac{4400}{2\mathrm{\pi }r} \\ =\frac{4400\times 7}{2\times 22\times 17.5} \\ =40\mathrm{cm} \end{gathered}$$
$$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{cylinder}=\mathrm{\pi }{r}^{2}h \\ =\frac{22}{7}\times 17.5\times 17.5\times 40 \\ =38500{\mathrm{cm}}^3 \end{gathered}$$