The Area of the shaded portion is given by (16 π -32) sq.inch, the correct option is A.
What is a Circle?
A circle is a round shaped figure whose all points lie in one plane and the distance between the center of the circle and all the points on the circle is constant.
The area of the shaded portion is equal to the difference of the area of the arc and  Area of the Triangle.
Area of an Arc =( [tex]\rm \theta[/tex] / 360) * π r²
Area = (90/360) * π * (8) ²
Area of the arc = 16 π sq.in
Area of the triangle = (1/2) * base * height
Area of the triangle = (1/2) * 8 * 8 = 32 sq.in
Area of the shaded portion = (16 π -32) sq.inch
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