The cost of fencing a circular field at the rate of ₹ 240 per metre is ₹ 52,800. The field is to be ploughed at the rate of ₹ 12.50 per m². Find the cost of ploughing the field.

Given:

Rate of fencing = ₹ 240 per metre

Total cost = ₹ 52,800

Let r be the radius of the field.

Total cost = Circumference of field x Rate of fencing

$⇒ 52,800 = 2πr \times 240\\[1em] ⇒ 2πr = \dfrac{52,800}{240}\\[1em] ⇒ 2πr = 220\\[1em] ⇒ 2 \times \dfrac{22}{7} \times r = 220\\[1em] ⇒ \dfrac{44}{7} \times r = 220\\[1em] ⇒ r = \dfrac{220 \times 7}{44}\\[1em] ⇒ r = \dfrac{5 \times 7}{1}\\[1em] ⇒ r = 35 \text{ m}$

Area of the field = πr²

$= \dfrac{22}{7} \times 35^2\\[1em] = \dfrac{22}{7} \times 1225\\[1em] = 22 \times 175\\[1em] = 3,850 \text{ m}^2$

Rate of ploughing = ₹ 12.50 per m²

Total cost of ploughing = Area of the field x Rate of ploughing

= 3,850 x 12.50

= ₹ 48,125

Hence, the total cost of ploughing is ₹ 48,125.