If areas of three circles are in ratio 4 : 9 : 25. What is the ratio of their radii?
Area of the circle of radius r is πr2
Answer: For the given ratio of areas of three circles 4 : 9 : 2, the ratio of the radii for three circles is r1 : r2 : r3 = 2 : 3 : 5
Let's find the ratio of their radii
Let the three circle be C1, C2 and C3 and r1, r2 and r3 be the radii of these three circles respectively.
We know that the formula to find the area of a circle using the radius r is πr2
Now we have been given with the fact that areas of these circles are in the ratio of 4 : 9 : 25
⇒πr12 : πr22 : πr32 = 4 : 9 : 25
Cancelling out the common factor π we get
⇒r12 : r22 : r32 = 4 : 9 : 25
⇒r12 : r22 : r32 = 22 : 32 : 52
⇒r1 : r2 : r3 = 2 : 3 : 5