The ratio of the area of a smaller circle to the bigger circle is 1:4. Find the ratio of radius of smaller circle to the bigger circle.

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Solution

As we know. area of a circle = $π r^{2}$

$\frac{Area of smaller circle}{Area of bigger circle} = \frac{1}{4}$

If $r_{1}$ be the radius of the smaller circle and $r_{2}$ be the radius of the bigger circle, then $\frac{π {r_{1}}^{2}}{π {r_{2}}^{2}} = \frac{1}{4}$
Hence, $\frac{r_{1}}{r_{2}} = \frac{1}{2}$

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The ratio of the area of a smaller circle to the bigger circle is 1:4. Find the ratio of radius of smaller circle to the bigger circle.

As we know. area of a circle = πr2 Area of smaller circle Area of bigger circle=14 If r1 be the radius of the smaller circle and r2 be the radius of the bigger circle, then πr12πr22=14 Hence, r1r2=12