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Question

A field is to be fenced on its boundary to protect its crop from animals roaming around. The field is shown in the following figure as a shaded region. If the rate of fencing is ₹ 25/m, then the total cost of fencing is ₹_____. (Use π=227)


  1. 800.00 
  2. 1044.5
  3. 41.78  
  4. 244.50 


Solution

The correct option is B 1044.5
Given:
Length of each line-segment = 16 m
Radius of each arc = 7 m
Angle of each arc = 40o



The green shaded region has two line-segments and two arcs of a circle.

Thus, Perimeter of the field
=length of two line segments+length of two arcs
=16+16+θ360×2πr+θ360×2πr

=32+2×40360×2×227×7

=32+9.78

=41.78 m

 Cost incurred
=Rate of fencing×perimeter of the field
=25×41.78
=1044.5

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