Q9 of 35 Page 311

A 7 meter wide path runs outside a circular park of Etalgacha Friends association club along perimeter. Let us write by calculating the area of path, if the perimeter of circular park is 352 meter, let us write by calculating how much cost for concreting the path at the rate of Rs. 20 per square meter.

Given, the perimeter of a circular park = 352 m


Width of a road outside circular park = 7 m


Now,


Perimeter of circle = 2πr where r is the radius of cirlce



⇒


⇒ 8 × 7 = 56 m


⇒ r = 56m


Inner radius of the park (r) = 56 m


Outer radius of the Park including the road (R) = width of circular path + r


R = 7 + 56 = 63 m


R = 63 m


Area of the road = π (R2 - r2) where R is the outer radius of the circle and r is the smaller radius of circle


= π(R + r) (R - r) [a2 - b2 = (a-b)(a-b)]


=


=


= 22 × 119


Area of the road = 2618 m2


Cost of concreting the path = area of path × rate of concreting the path per square meter


= 2618 × 20


= Rs 52360


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