Question 87317: I'm confused please help!!!!!
1.You have a sprinkler at city park that waters in a circular pattern. It shoots water out 40 feet from it's center and rotates in a circular pattern.
A. How many square feet are under the sprinkler?
B. If it is in the middle of a perfect square, how many acres are in each of the non-irrigated corners of the lawn.
For A. I got 5024 sq ft? Is this right? As for B, I have no idea how to work this out.
Answer by tutor_paul(519)   (Show Source):
You can put this solution on YOUR website! For problem A, you need to figure out the area of the circle. The equation for the area of a circle is:
In this case, you are given the radius of the circle (40 feet). So the area of the circle(Ac) is:
 square feet
 square feet
So, you got that part right!
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For Part B, you have a circle circumscribed inside a square (draw a square and fit a circle inside it to see what that looks like.) Now, since the sprinkler is going in a circular motion, there will be the corner sections of the square which will not be getting any water. This is the area (in acres) that they are asking you for.
To find this area, find the area of the square and subtract the area of the circle from that. The area of a square is the square of one side. You scan see from your drawing that one side of the square is equal to 2* radius of the circle. So, the area of the square (As) is given by:
 square feet.
To get the area of the unwatered (A)section, do the subtraction:
 square feet.
Note that they want the answer in acres, so you need to convert square feet to acres:
One acre = 43560 square feet, so you have:
 Acres
Note that this is the total unwatered area. The problem asks "how many acres are in each of the non-irrigated corners of the lawn?" To get that, you need to divide the above result by 4:
 Acres
Good Luck,
tutor_paul@yahoo.com
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