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NCERT Exemplar Solutions Class 10 Mathematics Solutions for Areas related to circles - Exercise 11.3 in Chapter 11 - Areas related to circles

Question 7 Areas related to circles - Exercise 11.3

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 r2θ

= ½ × (14)2 × (π/2)

= 154 m2

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

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