Question

The cost of fencing a circular field at the rate of Rs 24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per m2.

Answer 1

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Solution : 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 Fence

$\frac{Total Cost }{Rate}$

= $\frac{5280}{24}$

= 220

So , Circumference of field = 220 m

If r metre is the radius of the field

$2\pi r = 220$

$2 * \frac{22}{7} * r = 220$

$r = \frac{220*7}{2*22}$

$r = \frac{770}{2}$

r = 35

Area of the field

$\pi r^2 = \frac{22}{7} * 35 * 35$

$22 * 5 * 35m^2$

Total Cost of ploughing the field

Cost of 1 m^2 of the field = Rs. 0.50

Total Cost = 22 * 5 * 35 * 0.50

= Rs. 1925