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Question
The area between the circumference of two concentric circles is 2464cm2. If the inner circle has a circumference of 132cm, calculate the radius of the outer circle.
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Solution
We know,
The area of the ring between two concentric circles equal the area of the larger circle minus the area of smaller circle. Let the radius of the outer and inner ring be R and r respectively
The Area of a Circle with radius r = πr2
area of the ring between two concentric circle
= π(R2 - r2)
= 2464cm2
The Circumference of a Circle with radius r = 2πr
The Circumference of the inner Circle with radius r = 132
2πr = 132
⇒ r = 21cm
π(R2 - 212) = 2464
⇒ `(22)/(7)("R"^2 - 441)` = 2464
⇒ (R2 - 441) = 784
⇒ R2 = 1225
⇒ R = 35cm.
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