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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.
Solution
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.
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