Question

the cost of fencing a circular field at the rate to R.s 24/m square is R.s 5280 the field is to be ploughed at the rate of R.s 0.50/ m square. find the cost of ploughing the field.

Answer 1

Length of the fence (in metres) = Total cost / Rate = 5280/24 = 220
So, circumference of the field = 220 m
Therefore, if r metres is the radius of the field, then
2πr = 220

or, 2 × 22/7× r = 220
or, r = (220 × 7)/(2 × 22) = 35

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

Therefore, area of the field = πr2 = 22/7 × 35 × 35 m2 = 22 × 5 × 35 m2

Now, cost of ploughing 1 m2 of the field = Rs 0.50
So, total cost of ploughing the field = Rs 22 × 5 × 35 × 0.50 = Rs 1925

Answer 2

Length of the fence (in metres) = Total cost / Rate = 5280/24 = 220

So, circumference of the field = 220 m

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

2πr = 220

or, 2 × 22/7× r = 220

or, r = (220 × 7)/(2 × 22) = 35

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

Therefore, area of the field = πr2 = 22/7 × 35 × 35 m2 = 22 × 5 × 35 m2

Now, cost of ploughing 1 m2 of the field = Rs 0.50

So, total cost of ploughing the field = Rs 22 × 5 × 35 × 0.50 = Rs 1925