16

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 C_{1} and C_{2} with radii ‘r_{1}’ and ‘r_{2}’.

∵ Area of circle = πr^{2}

∴ Area of C_{1} = πr_{1}^{2}

and Area of C_{2} = πr_{2}^{2}

⇒ =

⇒ =

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 C _{1} and C_{2} is 2:3.__

16

17

A square is inscribed in a circle. Find the ratio of the areas of the circle and the square.

(view answer)