Question 324206: Can anyone help me with this word problem? A farmer has a square plot of land. An irrigation system can be installed with the option of one large circular sprinkler or nine small sprinklers. Which plan will provide water to the greatest percentage of land in the field regardless of cost or watering pattern?
Any help would be appreciated!!
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Can anyone help me with this word problem? A farmer has a square plot of land. An irrigation system can be installed with the option of one large circular sprinkler or nine small sprinklers. Which plan will provide water to the greatest percentage of land in the field regardless of cost or watering pattern?
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Let the sides of the square be 3s in length.
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With one circle, its diameter will be 3s.
With 9 circles, the diameter will be s.
The area of a circle is a function of the square of it diameter, so the area of the big circle is 9 times the area of one of the smaller circles.
The total area is the same.
It's the same for any number of circles, strange as that seems.
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