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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.

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39424 m^{2}

and ₹3942400

49896 m^{2}

and ₹4989600

10472 m^{2}

and ₹1047200

None of these

answer is C.

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Detailed 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 \times \frac{22}{7} \times r

\Rightarrow r = 112 m

Area of inner circle,

A_{1} = π r^{2} = \frac{22}{7} \times 112^{2} = 39424 m^{2}

Outer radius, R = r + 14 = 126 m
Area of outer circle,

A_{2} = π R^{2} = \frac{22}{7} \times 126^{2} = 49896 m^{2}

surface area of the road =

A_{2} - A_{1} = 10472 m^{2}

Cost of paving the road at Rs. 100 per square meter is ₹10472×100 = ₹1047200.
Hence, the area of the road is 10472

m^{2}

and the cost of paving it was Rs. 1047200.
So, Option 3 is correct.

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