Question

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

Answer 1

Let ABCD be a rectangular field.

Length of field = 20 m

Breadth of the field = 16 m

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 = `1/2` r²θ

= `1/2` × (14)² × (π/2)

= 154 m²

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