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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.

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Solution

## Suppose that the radius is r cm and the height is h cm.Here, curved surface area = 4400 cm2; circumference = 10 cm$\mathrm{Then}2\mathrm{\pi }rh=4400;2\mathrm{\pi }r=110\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.,110×h=4400\phantom{\rule{0ex}{0ex}}⇒h=4400÷110=40\mathrm{cm}\phantom{\rule{0ex}{0ex}}\mathrm{Also},2×\frac{22}{7}×r=110\phantom{\rule{0ex}{0ex}}⇒r\mathit{}=\frac{110×7}{2×22}=\frac{5×7}{2}=\frac{35}{2}\mathrm{cm}$$\therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}=\mathrm{\pi }{r}^{\mathit{2}}h\phantom{\rule{0ex}{0ex}}=\frac{22}{7}×\frac{35}{2}×\frac{35}{2}×40\phantom{\rule{0ex}{0ex}}=22×35×5×10=38500{\mathrm{cm}}^{3}$

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