Question

8. A horse is tied to a peg at one corner of a square
shaped grass field of side 20m by means of a 5 m
long rope (see Fig. 12.11). Find
(i) the area of that part of the field in which the
horse can graze.
(ii) the increase in the grazing area if the rope were
10 m long instead of 5 m. (Use t = 3.14)​

Answer 1

Answer:Side of square=15m

Length of rope=5m=radius

The area available for horse to graze is nothing but "Area of Quadrant of a circle'

∴ Area of Quadrant =  

4

π×r  

2

 

​  

=  

4

3.14×5×5

​  

 

=19.625m  

2

 

If the length of rope is increased to 10m then the new radius ,=10m

∴ Area of new quadrant =  

4

3.14×10×10

​  

 

=78.5m  

2

 

∴ Increase in grazing area =78.5−19.625=58.875m  

2