The cost of fencing a circular field at the rate of Rs. 24 per metre is Rs. 5820. Find

i) The radius of the circle

ii) The cost of ploughing the field at the rate of Rs. 2 per square metre.

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i) 25 , ii) Rs.5500

i) 35 , ii) Rs. 7700

i) 40 , ii) Rs. 8000

i) 45 , ii) Rs. 8800

answer is B.

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Detailed Solution

Concept: Firstly, equate the cost of circumference to the given cost to find the radius. Secondly, calculate the area of the circle and then multiply the area to the cost per metre square. Given: Cost of fencing per metre = Rs. 24
Cost of fencing a circular field = Rs. 5820.
Cost of ploughing per metre square = Rs. 2
Assume the radius of the circle to be r.
Therefore, Circumference of a circle = 2πr.
Cost of fencing per metre = Rs. 24
Cost of fencing 2πr metre = 2πr ×24
= 48πr
As given, the cost of fencing = Rs. 5280
But , 48πr=5280
⇒ r= 528048π
On solving, we get r = 35 metres
Hence, the radius of the circle is 35 m.
As we know, the area of the circle =πr2 Now, substituting the value of radius in the formula.
r2 = π352 ⇒ 3850 m2
As given, the cost of ploughing per square metre = Rs. 2
Cost of ploughing 3850 square metres = 2 ×3850
= Rs. 7700
Hence, the cost of ploughing the field = Rs. 7700
Hence, option 2 is correct.

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