The circumference of a circle is equal to the perimeter of a square. What is the ratio of the area of the circle to the area of the square? (The value of $\pi$ is $\frac{22}{7}$)

Explanation

Let the radius of the circle = (r) side of the square = (a) According to the question, circumference of the circle = perimeter of the square $$ 2\pi r = 4a $$ $$ \frac{r}{a} = \frac{4}{2\pi} $$ $$ \frac{r}{a} = \frac{2}{\pi} $$ ............(i) $$ \frac{Area of the circle (A_1)}{square of the circle (A_2)} = \frac{\pi r^2}{a^2} $$ $$ = \pi \left(\frac{r}{a}\right)^2 = \pi \times \frac{4}{\pi^2} = \frac{4}{\pi} $$ $$ = \frac{4 \times 7}{22} = 14 : 11 $$