yes, my professor only wrote the graph that I have on my paper on the board and told us to solve. It was very confusing because I am just learning the material but now I get what he was trying to say. The answer is 4piR^3/3 (as you can see I messed up on line after V =)....I agree that the information should have been more clear. Its times like these when I wonder why my professor is so against using a textbook. I will certainly be picking one up tomorrow.You need to describe your shape better. You don't label your axes, so we have no idea which is x and which is y. Plus, this is a volume, which means there needs to be a z-axis as well. Without that information we have to guess or reverse engineer work that you, yourself, are almost positive is wrong in order to figure it out. The best guess I can make is that it is a hemisphere, but if that were the case you would (should) know the final answer to compare against yours since the volume of a sphere is very well known (and easy to look up).
Looking at your final result, you have (R²-R) which is definitely wrong since you can't subtract a linear distance from an area.
thanks for the help, Im swamped in classes this semester so its been a long day. Im having trouble following what you are saying because of my inexperience but I think I fixed the issue. The mistakes I made were silly and I realized it after taking a little break. This is my final result.4piR^3/3 is the volume of a complete sphere, which is very inconsistent with the diagram which looks like it might be for a hemisphere.
But your set up is for a complete sphere.
Your problem is that you did the following
\(
\sqrt{R^2 \; - \; x^2} \; = \; R \; - \; x
\)
You then made another mistake when you tried to evaluate the limits.
You need to be more careful and pay close attention to the details.
Hi again,@HCN1996: I noticed that you removed your original image. That is discouraged because it makes it difficult, if not impossible, for readers of the thread to follow the discussion. Remember, this is not just about helping you and only you -- in fact the only reason that most responders take the time to do so is because they know they are potentially helping lots of people for years to come because of the archival nature of a forum such as this. It is extremely beneficial to students to see the mistakes that others have made and how they were found and fixed.
@MrAl: I agree with you that textual descriptions of steps being taken are very helpful and should be included -- if for no other reason than that it falls under the heading of the proper care and feeding of homework graders.
In the case of his sqrt() problem what his intended step was
\(
{\( \sqrt{R^2 \; - \; x^2} \)}^2 \; = \; R^2 \; - \; x^2
\)
which really doesn't warrant any explanation. He just messed up the math on something that he thought was simple and obvious (and thus not warranting an explanation).
What would have gone a long way toward making things clear would have been a well-labeled diagram that matched the problem (especially since the actual problem statement wasn't provided) and a sketch or at least textual description of the differential volume being integrated.
I was referring to that step in the original diagram -- I remember what he had in the original diagram because I commented on that exact error in Post #4.Hi again,
Yes, but like you said he removed his drawings and you happened to have commented on only the second diagram while i had commented on the first diagram he removed that went from:
sqrt(r^2-x^2)^2
to:
sqrt(r^2-x^2)
Here is a copy of his original diagram, enhance to help readability and a smaller file size for faster downloading and less archive space:
Huh? The first problem had the square root sign:Hello again,
Well, that is "if" there was a reasonable explanation. The first problem was the missing square root sign, and the second problem was the missing squares.
"If" there was a reasonable explanation then it should have been shown.
If it is just an error, that's a little different yes, but as i read it there always seemed to be something missing, and i think it started with the 2d diagram which doesnt explain how we ended up with a 3d formula
#2 happened because, in his mind, #1 cancelled them out.Hi,
That's not the expression, and i see this as two problems not just one.
The expression is (sqrt(R^2-x^2))^2
1. The square root sign disappears even though the outside square remains.
2. The individual squares disappear
The sqrt sign can disappear only if we apply the outside square, but then the inside squares must remain:
sqrt(R^2-x^2)^2 => R^2-x^2
and not as in the original paper:
sqrt(R^2-x^2)^2 => (R-x)^2
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