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Question
Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is `pih(2r+h)`
Solution
The width of the circular path = h
Let the inner circle be region A and the outer circle be region B
Radius of region A = r
Radius of region B = r + h
Area of the circular path = Area of region B − Area of region A
`= pi(r+h)^2-pir^2`
`= pi(r^2+h^2+2rh-r^2)`
`= pih(h+2r)`
Hence Proved
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