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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