If the radius and height of a cylinder are in the ratio $5 : 7$ and its volume is $550\, cm^{3}$, then its radius is equal to $\displaystyle \left(Take\, \pi\, =\, \frac{22}{7}\right)$

Let the radius be 5x and the height be 7x based on the given ratio of 5 to 7. Substituting these into the cylinder volume formula gives pi times the square of 5x times 7x equals 550, which simplifies to pi times 25x squared times 7x equals 550. Solving 175x cubed equals 550 divided by (22/7) gives x cubed equals 1, so x equals 1, making the actual radius 5 centimeters.

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