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A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see figure). Find the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use $\pi = 3.14$)
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Given:
A horse is tied to a peg at one corner of a square shaped grass field of side $15\ m$ by means of a $5\ m$ long rope.
To do:
We have to find the increase in the grazing area if the rope were 10 m long instead of 5 m.
Solution:
Length of the rope is increased from $5\ m$ to $10\ m$
This implies,
New radius of the sector grazed by the horse $= 10\ m$
Therefore,
Area grazed by the horse$=$ Area of the quadrant $( 10\ m)$
$=\frac{1}{4}\pi r^2$
$=\frac{1}{4}\times3.14\times(10)^2$
$=25\times3.14$
$=78.5\ m^2$
This implies,
Increase in the grazing area $=78.5-19.625$
$=58.875\ m^2$
Therefore, increase in the grazing area is $58.875\ m^2$.
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