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Question
A target shown in Fig. below consists of three concentric circles of radii, 3, 7 and 9 cm
respectively. A dart is thrown and lands on the target. What is the probability that the dart will land on the shaded region?
Solution
1st circle ⟶ with radius 3
2nd circle ⟶ with radius 7
3rd circle ⟶ with radius 9
Area of 1st circle =` (3)^2` = 9𝜋
Area of 2nd circle= `(7)^2` = 49𝜋
Area of 3rd circle = `(9)^2` = 81𝜋
Area of shaded region = Area of 2nd circle – area of 1st circle
= 49𝜋 – 9𝜋
= 40𝜋
Probability that will land on the shaded region =`"area of shaded region"/"area of 3rd circle"`= `(40pi) /(81pi) = 40/81`
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