Question

The curved surface area of a cylinder is 4400 cm² and the circumference of its base is 10 cm. Find the height and the volume of the cylinder.

Answer 1

Suppose that the radius is r cm and the height is h cm.
Here, curved surface area = 4400 cm²; circumference = 10 cm

$$\begin{gathered} \mathrm{Then}2\mathrm{\pi }rh=4400;2\mathrm{\pi }r=110 \\ \mathrm{i}.\mathrm{e}.,110\times h=4400 \\ \Rightarrow h=4400÷110=40\mathrm{cm} \\ \mathrm{Also},2\times \frac{22}{7}\times r=110 \\ \Rightarrow r\mathit{}=\frac{110\times 7}{2\times 22}=\frac{5\times 7}{2}=\frac{35}{2}\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}=\mathrm{\pi }{r}^{\mathit{2}}h \\ =\frac{22}{7}\times \frac{35}{2}\times \frac{35}{2}\times 40 \\ =22\times 35\times 5\times 10=38500{\mathrm{cm}}^3 \end{gathered}$$