Advertisement Remove all ads

Advertisement Remove all ads

Advertisement Remove all ads

Sum

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 .

Advertisement Remove all ads

#### Solution

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` r^{2}θ

= `1/2` × (14)^{2} × (π/2)

= 154 m^{2}

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

Concept: Areas of Sector and Segment of a Circle

Is there an error in this question or solution?