A field is in the form of a circle. A fence is to be erected around the field.
Question:

A field is in the form of a circle. A fence is to be erected around the field. The cost fencing would be Rs. 2640 at the rate of Rs. 12 per metre. The, the field is to be thoroughly ploughed at the cost of Re. 0.50 per m2. What is the amount required to plough the field? [Take π = 22/7].

Solution:

We know that the circumference C of a circle of radius r is

$C=2 \pi r$

It is given that cost of fencing around the circular field would be Rs.2640 at the rate of Rs.12 per meter. So,

$2 \pi r \times 12=2650$

$24 \times \frac{22}{7} r=2650$

$r=\frac{2650 \times 7}{24 \times 22}$

$=35 \mathrm{~m}$

We know that the area A of circle of radius r,

$A=\pi r^{2}$

Substituting the value of r

$A=\frac{22}{7} \times 35 \times 35$

$=3850 \mathrm{~m}^{2}$

Since, cost to plough per $\mathrm{m}^{2}$ field $=$ Rs. $0.50$

Then, cost to plough $3850 \mathrm{~m}^{2}$ field $=$ Rs. $0.50 \times 3850$

$=$ Rs. 1925

Hence, amount required to plough the field is Rs. 1925 .

 

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