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Question
A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m . If the length of the rope is increased by 5.5 m , find the increase in area of the grassy lawn in which the calf can graze .
Solution
The area grazed by the calf is in the form of a quadrant of a circle with radius 6 m.
Area grazed by the calf with rope 6 m=`1/4pi(6)^2`
`=28.28 m^2`
When the rope length is increased then total rope length = 6 + 5.5 m = 11.5 m
Area covered by the calf for grazing with rope `11.5 m=1/4pi(11.5)^2`
`=103.91 m^2`
Hence, increase in area of grassy lawn that is grazed = 103.91 − 28.28 = 75.63 m2
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