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)

- 800.00
- 1044.5
- 41.78
- 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

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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