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RD Chapter 15 Areas Related to Circles Ex 15.1 Solutions

Question - 31 : - Prove that the area of a circular path of uniform width surrounding a circular region of radius r is πh(2r + h).

Answer - 31 : -

Radius of inner circle = r
Width of path = h
Outerradius (R) = (r + h)
Areaof path = πR2 – πr2
= π {(r + h)2 – r2}
= π {r2 + h2 +2rh – r2}
= π {2rh + h2}
= πh (2r + h) Hence proved.

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