Question

The cost of fencing a circular field at the rate of Rs. 24 per meter is Rs. 5280. The field is ploughed at the rate of Rs. 0.50 per m². Find the cost of ploughing the field. (Take \( \pi = \frac{22}{7} \))

Hint:

To calculate the cost of ploughing a field, first calculate the area of the circle using the radius, and then multiply the area by the rate of ploughing per square meter.

Answer 1

Step 1: Find the circumference of the field.
We are given that the cost of fencing the circular field is Rs. 5280 at the rate of Rs. 24 per meter. The total cost of fencing is equal to the circumference of the circle multiplied by the rate per meter. Therefore, the circumference of the field is: \[ \text{Circumference} = \frac{\text{Total cost}}{\text{Rate per meter}} = \frac{5280}{24} = 220 \, \text{m} \]
Step 2: Use the formula for circumference to find the radius.
The formula for the circumference of a circle is given by: \[ C = 2\pi r \] Substitute the value of the circumference and \( \pi = \frac{22}{7} \): \[ 220 = 2 \times \frac{22}{7} \times r \] Solve for \( r \): \[ 220 = \frac{44}{7} \times r \] \[ r = \frac{220 \times 7}{44} = 35 \, \text{m} \]
Step 3: Find the area of the field.
The area of the circular field is given by: \[ A = \pi r^2 \] Substitute \( r = 35 \) and \( \pi = \frac{22}{7} \): \[ A = \frac{22}{7} \times 35^2 = \frac{22}{7} \times 1225 = 3850 \, \text{m}^2 \]
Step 4: Find the cost of ploughing the field.
The cost of ploughing the field is Rs. 0.50 per m². Therefore, the total cost of ploughing the field is: \[ \text{Cost of ploughing} = 0.50 \times 3850 = 1925 \, \text{Rs.} \]