Question:
The cost of fencing a circular field at the rate of Rs 25 per metre is Rs 5500. The field is to be ploughed at the rate of 50 paise per m2 . Find the cost of ploughing the field.$\left[\right.$ Take $\left.\pi=\frac{22}{7}\right]$
Solution:
Circumference $=\frac{\text { Total cost of fencing }}{\text { Rate of fencing }}=\frac{5500}{25}=220$
Let the radius of the circle be r.
Now,
Circumference $=220$
$\Rightarrow 2 \pi r=220$
$\Rightarrow r=35 \mathrm{~cm}$
Now,
Area of field $=\pi r^{2}=\frac{22}{7} \times(35)^{2}=3850 \mathrm{~cm}^{2}$
Cost of ploughing = Rate ⨯ Area of field = 0.5 ⨯ 3850 = Rs 1925
Hence, the cost of ploughing the field is Rs 1925.