Question

A chord of a circle of radius 28 cm subtends an angle of 45° at the centre of the circle. The area of the minor segment is
(a) 30.256 cm²
(b) 30.356 cm²
(c) 30.456 cm²
(d) 30.856 cm²

Answer 1

(d) 30.856 cm²
Let r be the radius of the circle and $\theta$ be the angle.
∴ Area of the minor segment $=\left(\frac{\mathrm{\pi }{r}^2\theta }{360}-\frac{1}{2}r\right)$ sin θ cm²

$$\begin{gathered} =\left|\left(\frac{22}{7}\times 28\times 28\times \frac{45}{360}\right)-\left(\frac{1}{2}\times 28\times 28\times \sin 45°\right)\right|{\mathrm{cm}}^2 \\ =\left|308-\left(392\times 0.707\right)\right|{\mathrm{cm}}^2 \\ =\left(308-277.144\right){\mathrm{cm}}^2 \\ =30.856{\mathrm{cm}}^2 \end{gathered}$$