4. The surface area of a circular pond is \( 616 \mathrm{~m}^{2} \). (a) Write the formula to find area of a circle. (b) Find the radius of the pond. (c) How many meters of wire is required to fence the pond? Find it. [1] (d) How much does it cost to fence the pond at the rate of Rs. 250 ner meter of wire? Find it.

(a) The formula to find the area of a circle is given by: \[ A = \pi r^2 \] where \( A \) is the area and \( r \) is the radius of the circle. (b) To find the radius of the pond, we can rearrange the area formula: \[ r^2 = \frac{A}{\pi} \] Given that the area \( A = 616 \, \mathrm{m}^2 \), we can substitute this value into the equation: \[ r^2 = \frac{616}{\pi} \] Using \( \pi \approx 3.14 \): \[ r^2 = \frac{616}{3.14} \approx 196 \] Now, taking the square root to find \( r \): \[ r = \sqrt{196} = 14 \, \mathrm{m} \] So, the radius of the pond is \( 14 \, \mathrm{m} \). (c) To find the amount of wire required to fence the pond, we need to calculate the circumference of the circle, which is given by the formula: \[ C = 2\pi r \] Substituting the radius we found: \[ C = 2 \pi (14) \approx 2 \times 3.14 \times 14 \approx 88 \, \mathrm{m} \] So, approximately \( 88 \, \mathrm{m} \) of wire is required to fence the pond. (d) To find the cost of fencing the pond at the rate of Rs. 250 per meter of wire, we can use the formula: \[ \text{Cost} = \text{Length of wire} \times \text{Rate per meter} \] Substituting the values: \[ \text{Cost} = 88 \, \mathrm{m} \times 250 \, \text{Rs/m} = 22000 \, \text{Rs} \] Thus, the cost to fence the pond is Rs. 22,000.