Question

A field is in the form of a circle. The cost of ploughing the field at Rs 1.50 per m^2 is Rs 5775. Find the cost of fencing the field at Rs 8.50 per m^2?

Answer 1

The cost of fencing field at Rs 8.50 per m^2 is Rs 1870

Solution:

Given that,

A field is in the form of a circle

The cost of ploughing the field at Rs 1.50 per m^2 is Rs 5775

The area of field is:

$Area = \frac{total\ cost}{rate}\\\\Area = \frac{5775}{1.50}\\\\Area = 3850\ m^2$

The area of circle is given as:

$Area = \pi r^2\\\\3850 = \pi r^2\\\\3850 = \frac{22}{7} \times r^2\\\\r^2 = 3850 \times \frac{7}{22}\\\\r^2 = 175 \times 7\\\\r^2 = 1225\\\\r = 35$

Find the circumference of circle:

$C = 2 \pi r\\\\C = 2 \times \frac{22}{7} \times 35\\\\C = 220\ m$

Find the cost of fencing the field at Rs 8.50 per m^2

$Cost = 220 \times 8.50\\\\Cost = 1870$

Thus the cost of fencing field is Rs 1870

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