Question 16 A cow is tethered to the corner of a rectangle, using a rope of length L.
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Question 16
A cow is tethered to the corner of a rectangle, using a rope of length L. The area of the rectangle is 154 sq. m.
What must be the estimated length of the rope, so that a cow can only graze one-fourth of the given area?
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Show answer & explanation
The cow grazes a quadrant of a circle of radius L. Equating (1/4)piL^2 to (1/4)154 gives piL^2 = 154, so L = 7 m.
Step-by-step Derivation:
Step 1: The corner of a rectangle has a 90 degree angle, so the grazing area is a quarter circle = (1/4) * pi * L^2.
Step 2: Given grazing area = (1/4) * 154 sq. m.
Step 3: (1/4) * pi * L^2 = (1/4) * 154 => pi * L^2 = 154.
Step 4: Using pi = 22/7: (22/7) * L^2 = 154 => L^2 = 154 * (7/22) = 49 => L = 7 m.