49
A chord of a circle of radius $14$ cm subtends an angle of $60^{\circ}$ at the centre. Find the area of the corresponding minor segment of the circle.
(Use $\pi = 3.14$ and $\sqrt{3} = 1.73$)
(Use $\pi = 3.14$ and $\sqrt{3} = 1.73$)
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Area of minor sector $= \frac{60}{360} \times 3.14 \times (14)^2 = 102.57$ (1)
Area of $\triangle AOB = \frac{1.73}{4} (14)^2 = 84.77$ (1)
Area of minor segment = Area of minor sector $-$ Area of $\triangle AOB$
$= 102.57-84.77 =17.8$ (1)
$\therefore$ Area of minor segment is $17.8$ cm$^2$
Area of $\triangle AOB = \frac{1.73}{4} (14)^2 = 84.77$ (1)
Area of minor segment = Area of minor sector $-$ Area of $\triangle AOB$
$= 102.57-84.77 =17.8$ (1)
$\therefore$ Area of minor segment is $17.8$ cm$^2$