Question

Question 8 (ii)
A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 12.11). Find:
(ii) The increase in the grazing area if the rope were 10 m long instead of 5 m. $(Use\pi =3.14)$

Answer 1

Side of square field = 15 m
Length of rope is the radius of the circle, r = 5 m
Since, the horse is tied at one end of square field; it will graze only quarter of the field with radius 5 m..
(ii) Area of circle if the length of rope is increased to $10m=\pi r^2=3.14\times {10}^2=314m^2$
Area of that part of the field in which the horse can graze
$=\frac{1}{4}$ of area of the circle
$=\frac{314}{4}=78.5m^2$
Increase in grazing area
$=78.5m^2-19.625m^2=58.875m^2$