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Question

In the figure given above, ¯¯¯¯¯¯¯¯AC is a diameter of the large circle and B lies on ¯¯¯¯¯¯¯¯AC so that ¯¯¯¯¯¯¯¯AB is a diameter of the small circle. If AB=1 and BC=2, Calculate the area of the shaded region.
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A
π4
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B
π
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C
2π
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D
9π4
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E
9π
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Solution

The correct option is C 2π
To find the area of the shaded region, we have to find the area of the bigger circle and the area of the smaller circle.
For large circle, AC is diameter measuring 3.
AC=AB+BC=1+2=3
Area of larger circle is = πR2
π(32)2=π94
Area of smaller circle is =πr2
π(12)2=π14
Area of shaded region is = Area of larger circle Area of smaller circle
=9π4π4
=9ππ4=8π4=2π

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