Question

The cost of fencing a circular field at the rate of Rs 24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per $m^2$. Find the cost of ploughing the field in Rupees. (Take $\pi =\frac{22}{7}$). [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

Lenght of the fence (in meters)

$=\frac{Totalcost}{Rate}=\frac{5280}{24}=220$

So,circumference of the field = 220 m

Therefore, if r meters is the radius of the field, then

$2\pi r=220$

$2\times \frac{22}{7}\times r=220$

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

i.e., radius of the field is 35 m.

Therefore, area of the field

$=\pi r^2=\frac{22}{7}\times 35\times 35=22\times 5\times 35m^2$

Now, cost of ploughing $1m^2$ of the field = Rs. 0.50

So, total cost of ploughing the field

$=Rs22\times 5\times 35\times 0.50=Rs.1925$