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In the adjoining figure a dart is thrown at the dart board and lands in the interior of the circle. What is the probability that the dart will land in the shaded region.
Ans: We have
AB = CD = 8 and AD = BC = 6
using Pythagoras Theorem is ? ABC, we have
AC2 = AB2 + BC2
AC2 = 82 + 62 = 100
AC = 10
OA = OC = 5 [ Q O is the midpoint of AC]
∴ Area of the circle = π (OA)2 = 25 π sq units [Q Area = π r2]
Area of rectangle ABCD = AB x BC = 8 x 6 = 48 sq units
Area of shaded region = Area of the circle - Area of rectangle ABCD Area of shaded region = 25 π - 48 sq unit.
Hence P (Dart lands in the shaded region) = Area of shaded region/Area of circle = 25π - 48/25π
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