In figure, the radii of three concentric circles are 14 cm, x cm and 56 cm, where 14 < x < 56. If four times the area enclosed between the two inner circles is equal to the area enclosed between the two outer circles, find the value of x.
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Answers
Given : , the radii of three concentric circles are 14 cm, x cm and 56 cm, where 14 < x < 56
four times the area enclosed between the two inner circles is equal to the area enclosed between the two outer circles,
To Find : Value of x
Solution:
Area of circle = πR²
area enclosed between the two inner circles = πx² - π(14)²
area enclosed between the two outer circles = π(56)² - πx²
π(56)² - πx² = 4 ( πx² - π(14)² )
=> π(56)² - πx² = 4πx² - 4π(14)²
=> 5πx² = π(56)² + 4π(14)²
=> 5x² = (56)² + 4(14)²
=> 5x² = (56)² + (28)²
=> 5x² = (28)² ( 4 + 1)
=> 5x² = (28)² ( 5)
=> x² = (28)²
=> x = 28
value of x = 28
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