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Mathematics

If the ratio of the areas of two circles is 25 : 4, then the ratio of their diameters is :

  1. 5 : 2

  2. 25 : 4

  3. 625 : 16

  4. 16 : 625

Mensuration

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Answer

Area of circle = πr2.

Given,

Ratio of areas of two circles = 25 : 4

πR12 : πR22 = 25 : 4

R12 : R22 = 25 : 4

Taking square root on both terms

R12:R22=25:4\sqrt{R1^2} : \sqrt{R2^2} = \sqrt{25} : \sqrt{4}

R1 : R2 = 5 : 2

Let R1 = 5a and R2 = 2a.

Diameter = 2 × Radius

D1 = 2 × R1 = 10a

D2 = 2 × R2 = 4a

D1 : D2 = 10a : 4a = 5 : 2.

Hence, option 1 is the correct option.

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