Find the area of the shaded portion in the figure if the diameter of the larger circle is 12 cm.
We need to find the area of the shaded part here. If we observe the figure, we can make out that the shaded region can be split into 2 semicircles, such that the diameter of the smaller semicircle is equal to the radius of the larger semicircle.
The radius of the larger semicircle R =d2 = 6 cm
The area of the larger semicircle is =12×π×R2 = 12×227×62 = 56.57 cm2
The radius of the smaller semicircle r = R2 = 3 cm
The area of the smaller semicircle = 12×π×32 = 12×227×9 = 14.14 cm2
Therefore,The area of the shaded region = Area of the larger semicircle +Area of the smaller semicircle = 56.57 + 14.14 = 70.71 cm2
The area of the shaded region is 70.71 cm2