Question

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 1

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 = `1/2 "r"^2θ` 

= `1/2 xx (14)^2 xx (π/2)`

= 154 m²

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