SOLUTION: A sprinkler is set in a corner of a rectangular lawn 10 feet by 25 feet. If the maximum distance the sprinkler can reach is ten feet, what percentage of the lawn will be watered f

Question 1199073: A sprinkler is set in a corner of a rectangular lawn 10 feet by 25 feet. If the maximum distance the sprinkler can reach is ten feet, what percentage of the lawn will be watered from this position?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let W = the width of the lawn = 25 ft
Let L = the length of the lawn = 10 ft
The sprinkler will cover one quadrant of a circle of radius = L
The area of the sprinkler's coverage is pi*L^2/4
The area of the rectangular lawn is W*L
The fraction of the lawn covered by the sprinkler is pi*L^2/4/(W*L) = pi*L/(4*W)
The percentage is therefore pi*10/(4*25)*100 = pi*10 = 31.4%
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