Question

The cost of fencing a circular field at the rate of Rs24 per meter is Rs5280. The field is to be ploughed at the rate of Rs1.5 per${m^2}$. Find the cost of ploughing the field.

Answer 1

Hint:In this question we first have to find the circumference of the field using the rate of fencing the field and the total cost. Then we need to find the radius using the circumference formula and finally proceed by finding the area and thus the cost of ploughing.

Complete step-by-step answer:

For Rs24, length of fencing = 1m

For Rs1, length of fencing = $\dfrac{1}{{24}}m$

For Rs5280, the length of fencing = $\dfrac{1}{{24}} \times 5280 = 220m$

Thus the circumference of the field = 220m

$ \Rightarrow 2\pi r = 220m$ , where r = radius of the field

$ \Rightarrow r = \dfrac{{220}}{{2\pi }} = \dfrac{{220}}{{2 \times \dfrac{{22}}{7}}} = \dfrac{{70}}{2} = 35m$

Now the area of the field = $\pi {r^2}$

$ \Rightarrow \dfrac{{22}}{7} \times {35^2} = 3850{m^2}$

Since the cost of ploughing = Rs0.50 per${m^2}$

Therefore total cost of ploughing the field = $Rs3850 \times 0.50 = Rs1925$

Hence, the cost is Rs1925.

Note-

We should remember to recall the formulas of area and perimeter of a circle while solving this question. Note that fencing is done on the circumference of the field while ploughing is done on the area of the circular field.