Question 5

Consider the circle shown below having angle AOB as $$135^\circ$$ and the shaded portion is the x part of the circular region. Calculate the value of x.

Solution

Area of both unshaded parts = $$\frac{\theta}{360^\circ} \times\pi r^2$$

= $$2\times\frac{135}{360}\times \pi r^2$$

= $$\frac{3}{4} \pi r^2$$

Area of complete circle = $$\pi r^2$$

$$\therefore$$ Area of shaded region = $$\pi r^2-\frac{3}{4} \pi r^2=\frac{1}{4} \pi r^2$$

=> Shaded portion is $$\frac{1}{4}$$ of circular region.

=> Ans - (D)

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