Question

A circle is inscribed in a square of side 14 m. The ratio of the area of the circle and that of
the square is

(a) $\mathit{\text{π}}$ : 3 (b) $\mathit{\text{π}}$ : 4 (c) $\mathit{\text{π}}$ : 2 (d) $\mathit{\text{π}}$ : 1

Answer 1

Let a and r be the side of the square and radius of the circle respectively.
Here, the diameter of the circle is equal to the side of the square. So
Diameter of circle = 2r = a
Therefore
$\frac{\mathrm{Area}\mathrm{of}\mathrm{circle}}{\mathrm{Area}\mathrm{of}\mathrm{square}}=\frac{\pi r^2}{a^2}=\frac{{\displaystyle \pi \times r^2}}{{\left(2r\right)}^2}=\frac{{\displaystyle \pi }}{4}$
Hence, the correct option is (b).