The radius and height of a cylinder are in the ratio $2 : 7$ If the curved surface area of the cylinder is $352$ sq.cm,find its radius.

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Solution

Let the radius be $2 x$ and height be $7 x$

Curved surface area $= 352$ sq.cm
$\Rightarrow 2 π r h = 352$

$\Rightarrow 2 \times \frac{22}{7} \times 2 x \times 7 x = 352$

$\Rightarrow 88 x^{2} = 352$

$\Rightarrow x^{2} = \frac{352}{88} = 4$

$∴ x = 2$

Hence radius $= 2 \times 2 = 4$ cm

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