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Word Problems

The ratio of ...

Question

The ratio of the areas of two concentric circles is $1 : 3$ . If the radius of the smaller is r, then the difference between the radii is best approximated by:

0.41

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0.73

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0.75

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0.73

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0.75

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Solution

The correct option is D $0.73$ r
Let x be the radius of the larger circle. Then $\frac{π r^{2}}{π x^{2}} = \frac{1}{3}, x = r \sqrt{3},$
$r \sqrt{3} - r = r (\sqrt{3} - 1) \sim 0.73 r$ .

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