MathematicsA road, 14m wide, surrounds a circular park whose circumference is 704m. Find the surface area of the road. Also, find the cost of paving the road at Rs. 100 per meter square.

A road, 14m wide, surrounds a circular park whose circumference is 704m. Find the surface area of the road. Also, find the cost of paving the road at Rs. 100 per meter square.


  1. A
    39424 m2 and ₹3942400
  2. B
    49896 m2 and ₹4989600
  3. C
    10472 m2 and ₹1047200
  4. D
    None of these 

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    Solution:

    Inner circle has the circumference of 704m and the circumference C of the circle with radius r is given by: C=2πr
    704=2×227×r
    r=112 m
    Area of inner circle, A1=πr2=227×1122=39424 m2
    Outer radius, R = r + 14 = 126 m
    Area of outer circle, A2=πR2=227×1262=49896 m2
    surface area of the road = A2-A1=10472 m2
    Cost of paving the road at Rs. 100 per square meter is ₹10472×100 = ₹1047200.
    Hence, the area of the road is 10472 m2 and the cost of paving it was Rs. 1047200.
    So, Option 3 is correct.
     
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