Question

What is the area of the region of the circle which is situated outside the inscribed square of side x?

(a) (π - 2)x²

(b) (π - 2)x²/2

(c) 2(π - 2)x²

(d) (π - 2)x²/4

Answer 1

(b) 

Diameter of the circle = AC 

= diagonal of the square = \(\sqrt2x\) cm

∴ Radius of the circle = \(\frac{\sqrt2x}{2}\) cm = \(\frac{x}{\sqrt2}\) cm

Hence, area of the circle = π(\(\frac{x}{\sqrt2}\))² cm²

= \(\frac{πx^2}{2}\) cm²

Area of the square = x²

∴ Required area = \(\frac{πx^2}{2}\) - x² = \(\frac{x^2}{2}\) (π - 2) cm².