Question

A wire bent in the form of a circle of radius 42 cm is cut and again bent in the form of a square. Find the ratio of the areas of the regions enclosed by the circle and the square.

Answer 1

Length of the wire = Circumference of the circle
= $\left(2\times \frac{22}{7}\times 42\right)=264$ cm
Therefore,
Perimeter of the square = Length of the wire = 264 cm
Hence, the side of the square = $\left(\frac{264}{4}\right)\mathrm{cm}=66\mathrm{cm}$
Thus,
Area of the circle = ${\mathrm{\pi r}}^2=\left(\frac{22}{7}\times 42\times 42\right)$ cm² = 5544 cm²
Area of the square = (Side)² = (66 cm)² = 4356 cm²

Therefore,

$\frac{\mathrm{Area}\mathrm{of}\mathrm{circle}}{\mathrm{Area}\mathrm{of}\mathrm{square}}=\frac{5544}{4356}=\frac{504}{396}=\frac{14}{11}$
Hence,
Area of circle : Area of square = 14 : 11