Find the area of the unwatered region to the nearest square meter.

eddy2017

eddy2017

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Hi, dearest professors, tutors and mere mortals like lev88 says:
I am working on this problem right now. I am attaching a drawing that comes with the problem. It has not bee npainted by me. It comes with it.
A farmer has a rectangle plot with sprinklers along the side. Each of the three water sprinklers covers a semicircle of 3 meters. the region shaded in yellow remains dry. Find the area of the unwatered region to the nearest square meter.

Solution
Given
Length = 18m
Width=4m
Area of the unwatered region=?
Each of the sprinklers covers a semicircle with a radius of 3m.
What I want to do first is to find the area of the whole rectangle. I think that is pretty evident because I have been given length and width and I have a r rectangular plot here.
So,
A= l* w
A=4m * 18m
A=72 m^2
Any hint now will be more than welcomed.
 

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Now subtract the area covered by the sprinklers. What is the area covered by one sprinkler? How about three sprinklers?
 
Jomo said:
Now subtract the area covered by the sprinklers. What is the area covered by one sprinkler? How about three sprinklers?
Click to expand...
Well, the length is 18 m, so one sprinkle takes up 6m, I guess. If one takes up 6, then the three sprinklers take up 18m.
 
eddy2017 said:
Well, the length is 18 m, so one sprinkle takes up 6m, I guess. If one takes up 6, then the three sprinklers take up 18m.
Click to expand...
You are talking nonsense again, sorry. The sprinkler puts out water into an area, a 2 dimensional area. The units of a 2 dimensional can be square feet, square inches, square meters. Note the square units??? Your area is 6m which is NOT an area. You need to think about what type of answer you might get and that answer must be square units.

There is a formula for the area of a circle. Please look it up and use that formula to find the area covered by the sprinkler system.
 
Another problem with your results is how would you compute 72m^2 - 18m? The units are different.
 
Here we go again. You read a problem, saw some numbers and shapes and decide to calculate the area of a rectangle. Why?

Let's say you need to move out of your apartment. What's the first thing you do? Do you look around, see a box and say: "Looks like it's big enough for my books, let's start packing"?
No! (Well, not likely)
You probably sit down and make a plan: 1. Find a new apartment 2. Hire movers 3. Sell/give away stuff you don't need 4. Pack 5. Switch services to new address. 6. Move
If this is the case, why not apply the same 'top down' approach to math?

You are asked to find the unwatered area. You even wrote "Area of the unwatered region=?", but then you completely forgot about it and noticed that it's easy to get the rectangular area ("pretty evident "). So what? Maybe we need it, maybe we don't. You need to complete "Area of the unwatered region=?" and only then do the necessary calculations.
 
I think i will use the formula for half a circle. It is what I have here. 3 half a circles or semicircles.
So,
72m-(1/2 pi r squared)
I got the length which is 18m all across.
I need to find the radius to solve for half the circle.
If I split 18 into three parts then I find that each of the half circles has a diameter of 6 .
The radius is half the diameter, so, each radius measures 3 meters, so I have the radius .
I'll plug it into the formula for a semicircle, taking into account that are 3 semicircles.

72- 3(1/2 pi 3²)
72-3(1/2 pi 9)
Let's simplify.
72-(3*0.5*3.14*9)
72-42.39
=29.6
This is the are covered by the sprinkler system.
So, now I will subtract this area from the total area of the plot to find the the area of the dry zone.
Okay?.
 
Last edited:
Lev, please, check this way I used. I will want to learn the other, but let me know if this one is right so far.
 
Last edited:
So I have to find the area of the unwatered region, but to the nearest square.
So before I do the subtraction, I round 29.6 to the nearest square meter.
30m².
Then I sub
72m²-30m²
=42 m²
The area which is dry.
 
And I remember now what professor Jomo taught me about square feet and meters.
There are 72 little squares on that plot each one is a meter long, of course , on each side.
 
lev888 said:
Here we go again. You read a problem, saw some numbers and shapes and decide to calculate the area of a rectangle. Why?

Let's say you need to move out of your apartment. What's the first thing you do? Do you look around, see a box and say: "Looks like it's big enough for my books, let's start packing"?
No! (Well, not likely)
You probably sit down and make a plan: 1. Find a new apartment 2. Hire movers 3. Sell/give away stuff you don't need 4. Pack 5. Switch services to new address. 6. Move
If this is the case, why not apply the same 'top down' approach to math?

You are asked to find the unwatered area. You even wrote "Area of the unwatered region=?", but then you completely forgot about it and noticed that it's easy to get the rectangular area ("pretty evident "). So what? Maybe we need it, maybe we don't. You need to complete "Area of the unwatered region=?" and only then do the necessary calculations.
Click to expand...
 
I have not gotten the usual like from you all. I hope everything is ok and you're not mad at me.
Thanks.
 
eddy2017 said:
So I have to find the area of the unwatered region, but to the nearest square.
So before I do the subtraction, I round 29.6 to the nearest square meter.
30m².
Then I sub
72m²-30m²
=42 m²
The area which is dry.
Click to expand...
Looks right. But I would not round until the end. In this case it doesn't matter, but in general the higher the precision of intermediate results, the lower the accumulated error.
 
lev888 said:
Looks right. But I would not round until the end. In this case it doesn't matter, but in general the higher the precision of intermediate results, the lower the accumulated error.
Click to expand...
Oh, ✅. thanks a lot. Thanks for the advice. I'll keep it in mind. And, if there is another way you would have done it, I would love to know.
 
lev888 said:
You do.
Click to expand...
Yes, I would. I read that you would have found the area of the unwatered region first. I have been thinking about how to do it that way. You call it top down math, like the normal thing to do. I am curious.
 
eddy2017 said:
Yes, I would. I read that you would have found the area of the unwatered region first. I have been thinking about how to do it that way. You call it top down math, like the normal thing to do. I am curious.
Click to expand...
No, not found - expressed!
Unwatered area = ?
 
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