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Prove that the area of a circular path of uniform width h surrounding a circular region of radius is πh(2r + h).

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Area of inner circle with radius r = πr

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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