# The radius and height of a cylinder are in the ratio 5:7 and its volume is 550cm^3. Find its radius .

Solution: Let the radius of the base and height of the cylinder be 5$x$ cm and 7$x$ cm respectively. Then,

Volume $=\pi r^2h$ $=550 cm^3$

$=\frac{22}{7} \times (5x)^2 \times 7x = 550$

$\Rightarrow$                       $\frac{22}{7}\times 25x^2 \times 7x= 550\Rightarrow 22\times 25x^3=550$

$\Rightarrow$                     $550x^3=550\Rightarrow x^3=1\Rightarrow x=1cm$

Hence , radius of the cylinder = 5$x$ cm = $(5\times1)cm=5cm.$

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