Question

The cost of ploughing a circular field at the rate of Rs. 0.25 per square metre is Rs. 3850.Find the cost of fencing the field at Rs.15 per metre.

Answer 1

$let \: the \: radius \: of \: the \: cirular \: field \: = r \\ \\ therefore \: area \: of \: circular \: field = \pi \times r {}^{2} \\ \\ since \: the \: cost \: of \: ploughing \: the \: circular \: field = 3850 \: rupee \\ \\ therefore \: according \: question \\ \\ \pi \times r {}^{2} \times 0.25 = 3850 \\ \\ \pi \times r {}^{2} = \frac{3850}{0.25} = \frac{385000}{25} = 15400 \\ \\ = > \frac{22}{7} \times r {}^{2} = 15400 \\ \\ = > r {}^{2} = \frac{15400 \times 7}{22} \\ \\ = > r {}^{2} = 4900 \\ \\ = > r = \sqrt{4900} = 70m \\ \\ therefore \: circumferene \: of \: the \: circle \\ \\ = 2\pi \times r \\ \\ = 2 \times \frac{22}{7} \times 70 \\ \\ = 44 \times 10 = 440 \: m \\ \\ since \: the \: cost \: of \: fencing \: of \: 1 \: m = 15 \: rupees \\ \\ therefore \: cost \: of \: fencing \: of \: the \: circular \: field \\ \\ = 440 \times 15 \\ \\ = 6600 \: rupees$

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Answer 2

The cost of fencing the field at Rs.15 per metre is Rs.6600

Step-by-step explanation:

The cost of ploughing a circular field at the rate of Rs. 0.25 per square metre  is Rs. 3850.

So, Area ploughed =$\frac{3850}{0.25}=15400 sq.m.$

The field is circular

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

So, $\pi r^2 = 15400$

$\frac{22}{7} \times r^2 = 15400$

$r^2 = \frac{15400 \times 7}{22}$

$r=\sqrt{\frac{15400 \times 7}{22}}$

r=70

So, radius of field is 70 m

Circumference of circular field =$2 \pi r= 2 \times \frac{22}{7} \times 70=440 m$

Cost of fencing 1 m = Rs.15

Cost of fencing 440 m =$440 \times 15 = Rs.6600$

Hence the cost of fencing the field at Rs.15 per metre is Rs.6600

#Learn more:

Cost of ploughing at the rate of Rs 10 per metre square is Rs 1540 find the radius of the circular field

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