SOLUTION: I am lost can you please
You have a sprinkler at City Park that waters in a circular pattern as below. It shoots water out 40 feet from its center and rotates in a circular pa
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Question 224624: I am lost can you please
You have a sprinkler at City Park that waters in a circular pattern as below. It shoots water out 40 feet from its 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?
Found 2 solutions by ankor@dixie-net.com, Greek2Me:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
ou have a sprinkler at City Park that waters in a circular pattern as below. It shoots water out 40 feet from its center and rotates in a circular pattern.
:
A. How many square feet are under the sprinkler?
Find the area of a circle with a radius of 40'
A =
A = 5026.55 sq/ft
:
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?
The side of the square would be equal to the diameter of the circle inside it, 80'
A = 80^2
A = 6400 sq/ft is the area of the square
then
6400 - 5026.55 = 1373.45 sq/ft inside the square is unsprinkled
:
But it wants to know in acres, convert sq ft to acres
2.296(10^-5) * 1373.45 = .03153 acres unsprinkled
In each corner: = .0079 acres
Answer by Greek2Me(1) (Show Source): You can put this solution on YOUR website!
Your FIRST question is actually "What is the area of a circle with a 40 foot radius?" Many people can casually quote "Pie are square", (well actually its πR^2), but most don't know that it's actually the equation to calculate the area of a circle. Pi (the mathematical symbol is π) is an endless "never repeating" number that is roughly 3.14159, "R" is the radius of a circle or arc and 2 (or "squared") is any number times itself.
Whenever we have an "unknown" in a equation we use "X" as a placeholder for it. So, using the formula above, we would state our question mathematically by plugging in the radius to say: X = 3.14159 * 40^2
If your calculator has a couple of "special" buttons on it, this will be REALLY easy. One is the Pi symbol (remember, it looks like this: π). The other may have something like ^2 printed on it. That means "raised to the power of 2", or "squared".
If you DO have these buttons, you can enter your equation like this:
π * 40^2 =
and get your result.
If you only have a basic calculator and DON'T have the special buttons, you can do it like this:
3.14159 * 40 * 40
and get the same thing.
The SECOND question involves subtracting the area of one geometric figure (the circle) from another one (the square). Since you know the radius of the circle (40 feet), you know that the side of the square is equal to the diameter of the circle (or TWICE the radius). The formula for the area of a square is simply "the length of the side squared", or S^2.
Since the side of the square is 80 (two times the radius), you enter:
80^2
to get the area of the square. Now, if you subtract the area of the circle (from the first problem) from the area of the square, the only thing LEFT is the corners! But be careful! The answer to your FIRST question was in square feet, but the second question asked for an answer in ACRES!
No problem. One acre is equal to 43560 square feet, so if we divide our answer (above) by 43560, that will give us our final answer in acres.
Now, I was pretty careful to tell you HOW to do it, without telling you what the answer actually WAS. If you paid attention, you should have no problem plugging in the numbers for the answer. Good luck.
"Give a man a fish, feed him for a day. TEACH a man to fish, feed him for a lifetime!"
RMc
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