Question

A field is in the form of a circle. A fence is to be erected around the field. The cost of fencing would be Rs.5280 at the rate of Rs.24 per metre. Then, the field is to be throughly ploughed at the cost of $Rs.0.50per{m}^2$. What is the amount required to plough the field?

Answer 1

Given cost of fence per $=$Rs. $24$

Total cost of fence around the field $=$ Rs. $5280$

i.e., $2\pi r\times 24=5280$

$2\times \frac{22}{7}\times r=\frac{5280}{24}$

$2\times \frac{22}{7}\times r=22$

$r=\frac{7}{2}=3.5$

Area of the field $=\pi r^2$

$=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}=\frac{77}{2}$

cost of ploughing the field $=0.50$ per $m^2$

$\therefore$ Cost of ploughing the whole field $=\frac{77}{2}\times \frac{1}{2}$

$=\frac{77}{4}$.