15.A target consists of three concentric circles of radii 5 cm , x cm , 10 cm
respectively. If the probability that the dart thrown lands on the green region
is 39 / 100 , find x.
Answers
Given : A target consists of three concentric circles of radii 5 cm , x cm , 10 cm respectively. Probability that the dart thrown lands on the green region is 39 / 100
To find : Value of x
Solution:
Area of circle with radius 5 cm = π (5)² = 25 π cm²
Area of circle with radius x cm = π (x)² = x² π cm²
Area of circle with radius 10 cm = π (10)² = 100 π cm²
Total area = 100 π cm²
Green region is the region between circle of radius 5 cm & x cm
Area of green region = x² π - 25 π cm²
Probability = (x² π - 25 π) / 100 π = 39/00
=> x² - 25 = 39
=> x² = 64
=> x = 8
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