The area of two circles are in the ratio 9:6, find the ratio of their circumferences.
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The area of two circles are in the ratio 9:6, find the ratio of their circumferences.
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1st Case :-. 2nd case :-
let radius = r. let radius = R
A.T.Q
Area of 1st circle. 9
-------------------------. = ------
Area of 2nd circle. 6
πr². 9
------. =. -----
πR². 6
r². 9
-----. =. ------
R². 6
r. √9
------ =. --------
R. √6
r. 3
-----. =. -------
R. ✓6
So, r:R = 3:✓6
Perimeter of 1st circle. 2πr
---------------------------------. = ----------
Perimeter of 2nd circle. 2πR
so, Perimeter of 1st circle. 3
---------------------------------. =. -----
Perimeter of 2nd circle. ✓6
so , required ratio =. 3:✓6