Question

A circular park whose circumference is 352 meters is surrounded by a road.If the area of the road is 2618 sq m , calculate the width of the road .

Answer 1

given, 
      circumference of a circular park = 352m
      area of the road = 2618 m² 
proof,
     circumference of a circle = 2×22/7×r
     352 = 2×22/7×r
     (352×7) / (22×2) = r
     56 m = r
    
     area of the circle =22/7×r²
     area of the circular park = 22/7×56×56
                                            =  22×8×56
                                            = 9856 m²
     area of the of the circular road = 2618 m²
     radius of the park + width of the road =  bigger radius 
     let us take the bigger radius = a
     than,
            a = 56+ width of the road
     area of the bigger circle(road+park) = area of the park+area of the road
     area of the bigger circle(road+park) = 9856+2618
                                                               = 12474 m²
     
     area of the bigger circle(road+park) = 22/7×r²
     12474 =22/7×a²
     (12474 × 7) / 22 = a²
     3969 = a²
     63 = a (radius of the bigger circle)
    
     radius of the bigger circle - radius of the park = width of the road
     63 - 56 = 7
     therefore, the width of the road = 7 m