Question

Calculate the area of the shaded region in the figure common between two quadrants of circle of radius 16cm each.​

Answer 1

Answer:

Area of shaded region= Area of the first quadrant + Area of the second quadrant − Area of the square.

That is,  $\frac{\theta}{360} \times \pi r^{2} + \frac{\theta}{360} \times \pi r^{2} - side^{2}.$

$\to 2(\frac{\theta}{360} \times \pi r^{2}) - side^{2}.$

$\to 2 \times \frac{90}{360} \times 3.14 \times 16^{2} -16^{2} .$

$\to 0.5 \times 3.14 \times 256-256$

$\to 1.57 \times 256 - 256$

$\to 145.92 \: cm^{2} .$

We just calculated the area of the shaded region, but it is overlapped by the two circles. Thus, we need to divide the area by 2×2 = 4.

$\to 145.92 \div 4 = 36.48 cm^{2}$

AREA OF THE SHADED REGION = 36.48 cm².

HOPE THIS HELPS :D