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

Sum

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

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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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APPEARS IN

RD Sharma Class 10 Maths
Chapter 13 Areas Related to Circles
Exercise 13.1 | Q 31 | Page 13
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