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In the adjoining figure,
$\triangle OAB$ is an equilateral triangle and the area of the shaded region is $750 \pi$ cm$^2$.
Find the perimeter of the shaded region.
$\triangle OAB$ is an equilateral triangle and the area of the shaded region is $750 \pi$ cm$^2$.
Find the perimeter of the shaded region.
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$\angle AOB = 60^\circ$ (1/2 Mark)
Thus, angle of sector corresponding to shaded region = $300^\circ$ (1 Mark)
So, $\frac{300}{360} \pi r^2 = 750\pi$ (1 Mark)
$r^2 = 900$
$r = 30$ cm (1 Mark)
Perimeter of shaded region = $\frac{300}{360} \times 2 \times \pi \times 30 + 2 \times 30$ (1/2 Mark)
$= 50\pi + 60 = \frac{1520}{7}$ cm
Thus, angle of sector corresponding to shaded region = $300^\circ$ (1 Mark)
So, $\frac{300}{360} \pi r^2 = 750\pi$ (1 Mark)
$r^2 = 900$
$r = 30$ cm (1 Mark)
Perimeter of shaded region = $\frac{300}{360} \times 2 \times \pi \times 30 + 2 \times 30$ (1/2 Mark)
$= 50\pi + 60 = \frac{1520}{7}$ cm