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

Answer:

Let ABCD be a rectangular field.

Length of field = 20 m

Breadth of the field = 16 m

According to the question,

A cow is tied at a point A.

Let length of rope be AE = 14 m = *l*.

Angle subtended at the center of the sector = 90°

Angle subtended at the center (in radians) θ = 90π/180 = π/2

∴ Area of a sector of a circle = ½ r^{2}θ

= ½ × (14)^{2} × (π/2)

= 154 m^{2}

Hence, the required area of a sector of a circle is 154 m^{2.}

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