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Question

If the ratio of the areas of two circles is 1:4, then the ratio of their circumferences is ...................

A
1:4
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B
2:3
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C
1:2
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D
3:2
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Solution

The correct option is D 1:2
For 1st circle, radius =r1, circumference =C1, Area =A1
For 2nd circle, radius =r2, circumference =C2, Area =A2
Given, A1A2=14π(r1)2π(r2)2=14r1r2=12.....(1)
Now,
C1C2=2πr12πr2=r1r2=12 ........ [by (1)]
Hence, ratio of circumference of circles is 1:2

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