Q11 of 68 Page 15

Prove that the area of a circular path of uniform width h surrounding a circular region of radius is.


Area of inner circle with radius r = πr2


Radius of outer circle = r+h


Area of outer circle = π(r+h)2


Area of circular path with width = h


= π(r+h)2 – πr2


By using (a+b)2 = a2 + b2 +2ab


= π(r2 + h2 + 2rh) – πr2


=πr2 + πh2 + 2πrh – πr2


= πh(2r+h)… Proved


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