Area 6
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Problem: The area of the ring between two concentric circles is 1694 sq. cm.
If the width of the ring is 7 cm, find the radii of the circles.
Solution: Let the radius of the inner circle be x cm
Radius of the outer circle is (x + 7)cm
Area of the ring = Π[(x + 7)2 - x2] cm2
= Π(2x + 7)(7) cm2
∴ Π(2x + 7)(7) = 1694
2x + 7 = 1694 × 7/22 × 1/7 = 77
2x + 7 = 77
2x = 77 – 7
2x = 70
⇒ x = 70/2 = 35
∴ Radius of the inner circle is 35 cm and that of the outer circle is 35 + 7 = 42 cm.
