The areas of two circles are in the ratio 4:9. What is the ratio between their circumferences?
Given:
Ratio of areas of two circles = 2:3
Let the two circles be C1 and C2 with radii ‘r1’ and ‘r2’.
∵ Area of circle = πr2
∴ Area of C1 = πr12
and Area of C2 = πr22
⇒ =
⇒ =
Taking square root on both sides, we get
⇒ =
⇒ =
Multiplying and dividing L.H.S. by ‘π’, we get
⇒ =
Multiplying and dividing L.H.S. by ‘2’, we get
⇒ =
As Circumference of circle = 2πr
⇒ =
Hence, the ratio between the circumferences of C1 and C2 is 2:3.
A square is inscribed in a circle. Find the ratio of the areas of the circle and the square.
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