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The cost of fencing a circular field at the rate of Rs.36 per metre is Rs.11880. The field is to be ploughed at the rate of Rs. 0.60 per sq.m. Find the cost of ploughing the field.

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1 Answer

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Total cost of fencing a circular field = Rs. 11880

Cost of fencing per meter = Rs. 36

\(= \frac{11880}{36}\)

= 330

Here, Total length of the field would be circumference of the circular field.

Total length = Circumference of circular field

\(330 = 2\pi r\)

\(2 \times \frac{22}{7} \times r = 330\)

\(\frac{44 \times r}{7} = 330\)

\(r = \frac{330 \times 7}{44}\)

r = 52.5 m

Now,

Area of circular field = \(\pi r^2\)

\(= \frac{22}{7} \times (52.5)^2\)

\(= \frac{22}{7} \times 52.5 \times 52.5\)

= 22 x 7.5 x 52.5 m2

= 8662.5 m2

Now, Cost of ploughing 1 m2 of the field = Rs 0.60

Cost of ploughing 8662.5 m2 of the field = Rs. 0.60 x 8662.5 = Rs. 5197.5

Hence, cost of ploughing the field = Rs. 5197.5

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