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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 ╧Аh(2r + h).

Answer - 31 : -

Radius of inner circle = r
Width of path = h
тИ┤ Outerradius (R) = (r + h)
тИ┤ Areaof path = ╧АR2┬атАУ ╧Аr2
= ╧А {(r + h)2┬атАУ r2}
= ╧А {r2┬а+ h2┬а+2rh тАУ r2}
= ╧А {2rh + h2}
= ╧Аh (2r + h) Hence proved.

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