Figure, ABCD is a square of side 2a. Find the ratio between the circumferences and the areas of the incircle and the circum-circle of the square.

Explanation

The diameter of inner circle is 2a
The radius is a

The diameter of outer circle is `2sqrt(2)a`

Therefore radius of outer circle `sqrt(2)a`

The circumference of inner circle is=` 2 xx pi xx 2a =4 xx pi xx a`

The circumference of outer circle is=` 2 xx pi xx sqrt(2)a`

ratio between the circumferences of the inner circle and outer circle= `(4 xx pi xx a)/(2 xx pi xx sqrt(2)a)= 1 : sqrt(2)`

The area of inner circle =` pi xx (a)^2 = pi xx a^2`

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