Q. 10

A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m × 16 m. Find the area of the field in which the cow can graze.

Answer :

Given: Length of rope = 14 m


Length of field = 20 m


Breadth of a filed = 16 m


To find: Area of field for cow to graze.


Explanation:



Let ABCD be a rectangular field.


Length of field = 20 m


Breadth of the field = 16 m


Suppose a cow is tied at a point A.


Let length of rope be AE = 14 m = l (say).


Angle subtended at the centre of the sector = 90°


Angle subtended at the centre (in radians) θ = 90π/180


= π/2


Area of a sector of a circle



= 154 m2


Hence, the required area of a sector of a circle is 154 m2.


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