The circumference of a circular garden is 572 m.Outside the garden a road, 3.5 m wide runs around it.Calculate the cost of repairing the road at the rate of Rs. 375 per 100 sq. m.

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Solution

Let the radius of garden be = $R_{1}$ m and radius of garden with road outside be = $R_{2} m$ .
$2 \times π \times R_{1} = 572 m$ . (given)
$\leftarrow R_{1} = 91 m$
$R_{2} = 91 + 3.5 = 94.5 m$ (road width is 3.5 m)

Area of garden $= π \times R 1^{2} = π \times 91^{2} s q .$ m; Area of garden with road = $π \times {94.5}^{2} s q . m$
Therefore, area of the road = $π \times {94.5}^{2} - π \times 91^{2} = π \times (94.5 + 91) (94.5 - 91)$
$= π \times 185.5 \times 3.5 = 2040.5 s q . m$
Cost of repairing the road is Rs 375 per 100 sq.m.
Total cost of repair = $\frac{375}{100} \times 2040.5 = R s 7651. 88$

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