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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
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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 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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