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 $\pi =\frac{22}{7}$)

• A. 41.78
• B. 244.50
• C. 800.00
• D. 1044.5

Answer 1

The correct option is D 1044.5

Given:
Length of each line-segment = 16 m
Radius of each arc = 7 m
Angle of each arc = ${40}^o$



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

Thus, Perimeter of the field
$=lengthoftwolinesegments+lengthoftwoarcs$
$=16+16+\frac{\theta }{360}\times 2\pi r+\frac{\theta }{360}\times 2\pi r$

$=32+2\times \frac{40}{360}\times 2\times \frac{22}{7}\times 7$

$=32+9.78$

$=41.78m$

$\therefore$ Cost incurred
$=Rateoffencing\times perimeterofthefield$
$=25\times 41.78$
$=₹1044.5$