A circular park is surrounded by a road 21, m | vedclass

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(B) Given that,a circular park is surrounded by a road.Width of the road $= 21\, m$.Radius of the park $(r_i) = 105\, m$.Therefore,the radius of the w

Vedclass · Accepted Answer

$15246$

Vedclass · Answer

(B) Given that,a circular park is surrounded by a road.Width of the road $= 21\, m$.Radius of the park $(r_i) = 105\, m$.Therefore,the radius of the whole circular portion (park + road) is $r_e = 105 + 21 = 126\, m$.Now,the area of the road $=$ Area of the whole circular portion $-$ Area of the circular park.Area of road $= \pi r_e^2 - \pi r_i^2 = \pi(r_e^2 - r_i^2)$.Using the identity $a^2 - b^2 = (a - b)(a + b)$:Area of road $= \frac{22}{7} 	imes (126^2 - 105^2) = \frac{22}{7} 	imes (126 + 105)(126 - 105)$.Area of road $= \frac{22}{7} 	imes 231 	imes 21$.Area of road $= 22 	imes 231 	imes 3 = 15246\, m^2$.Hence,the required area of the road is $15246\, m^2$.

$A$ circular park is surrounded by a road $21\, m$ wide. If the radius of the park is $105\, m$,find the area of the road in $m^2$.

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