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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.

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Solution

Given: A calf is tied with a rope of length 6m at the corner of a square grassy lawn of side 20m.

So, radius of quadrant DPQD (r) = length of rope = 6 m

Therefore,

Area of sector DPQD=πr2θ3600

=3.14×(6)2×9003600

=0.785×36=28.26m2

Now, if the length of the rope is increased by 5.5 m

So, total length of the rope (R) = 6 + 5.5 = 11.5 m

Area of sector DRSD=πR2θ3600

=3.14×(11.5)2×9003600

=0.785×132.25=103.81625m2

Therefore,

Increased area = Area of sector DRSD – Area of sector DPQD

= 103.81625 – 28.26

= 75.55625 m2

= 75.56 m2

Hence, the increase in area of the grassy lawn is 75.56 m2.


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