How to find the volume of a sphere [spherical coordinates]

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The discussion focuses on finding the volume of a hemisphere using spherical coordinates, with participants questioning the accuracy of calculations and the use of limits. There are concerns about potential mistakes in the mathematical steps, particularly regarding subtraction versus multiplication and the correctness of cosine values. Participants also express frustration over an incomplete integral step and the ambiguity of terms like "a" and "r" in related threads. Additionally, there is a reminder to adhere to forum etiquette by not opening multiple threads on the same topic and maintaining the homework template for clarity. The thread concludes with a note that it has been closed due to these issues.
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i don't know to using limit of r ?
 

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i'm sorry i mean hemi-sphere of : sqrt[x^2+y^2+(z-a)^2] = R
 
I think there are mistakes between line 3 and 4. Where did you get the subtraction from? Shouldn't it be a multiplication? Also the cosine values seem wrong. And finally, why did you stop at the easiest of all integrals at the end ##\int r^2dr## from ##r= 0## to ?
 
Please do not open more than one thread with the same topic, especially if the two are both ambiguous: with or without cone, what is ##a## needed for and what is ##r## in your other thread. Furthermore, do not delete the homework template, use it! It makes reading a lot easier and if you delete it, it can be viewed as disrespectful to those who are willing to answer.

Thread closed.
The duplicate is https://www.physicsforums.com/threads/how-to-find-hemi-sphere-on-the-cone.939376/#post-5938849
 

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