Given the cylinder $(x-1)^2+y^2 leq1$ and a sphere centred at $(0,0,0)$ with radius $2$, find the volume of...












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I attempted this using cylindrical co-ordinates but I am not sure if my attempt is correct. This is what I have:
equation of sphere : $x^2+y^2+z^2=4,$ cylindrical coordinates this is $z^2=4-r^2$ leading to:
$$0.25V= int_0^{pi/2} int_0^1 rsqrt{4-r^2} ,drdvartheta$$










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  • $begingroup$
    Use $pi$ for $pi$ and use $sqrt{wxyz}$ for $sqrt{wxyz}$.
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:41










  • $begingroup$
    This is called MathJax, a type of $LaTeX$. It works in the title section too.
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:42










  • $begingroup$
    Please edit the question accordingly :)
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:42










  • $begingroup$
    It might help to include what steps you took to get your answer, since what's important when studying Mathematics is not so much the answers to questions, but the reasons why they are the answers. Again, please edit the question.
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:44


















0












$begingroup$


I attempted this using cylindrical co-ordinates but I am not sure if my attempt is correct. This is what I have:
equation of sphere : $x^2+y^2+z^2=4,$ cylindrical coordinates this is $z^2=4-r^2$ leading to:
$$0.25V= int_0^{pi/2} int_0^1 rsqrt{4-r^2} ,drdvartheta$$










share|cite|improve this question











$endgroup$












  • $begingroup$
    Use $pi$ for $pi$ and use $sqrt{wxyz}$ for $sqrt{wxyz}$.
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:41










  • $begingroup$
    This is called MathJax, a type of $LaTeX$. It works in the title section too.
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:42










  • $begingroup$
    Please edit the question accordingly :)
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:42










  • $begingroup$
    It might help to include what steps you took to get your answer, since what's important when studying Mathematics is not so much the answers to questions, but the reasons why they are the answers. Again, please edit the question.
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:44
















0












0








0


0



$begingroup$


I attempted this using cylindrical co-ordinates but I am not sure if my attempt is correct. This is what I have:
equation of sphere : $x^2+y^2+z^2=4,$ cylindrical coordinates this is $z^2=4-r^2$ leading to:
$$0.25V= int_0^{pi/2} int_0^1 rsqrt{4-r^2} ,drdvartheta$$










share|cite|improve this question











$endgroup$




I attempted this using cylindrical co-ordinates but I am not sure if my attempt is correct. This is what I have:
equation of sphere : $x^2+y^2+z^2=4,$ cylindrical coordinates this is $z^2=4-r^2$ leading to:
$$0.25V= int_0^{pi/2} int_0^1 rsqrt{4-r^2} ,drdvartheta$$







calculus volume






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 8 '18 at 19:54









Shaun

9,050113682




9,050113682










asked Dec 8 '18 at 19:38









recursive functionrecursive function

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41












  • $begingroup$
    Use $pi$ for $pi$ and use $sqrt{wxyz}$ for $sqrt{wxyz}$.
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:41










  • $begingroup$
    This is called MathJax, a type of $LaTeX$. It works in the title section too.
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:42










  • $begingroup$
    Please edit the question accordingly :)
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:42










  • $begingroup$
    It might help to include what steps you took to get your answer, since what's important when studying Mathematics is not so much the answers to questions, but the reasons why they are the answers. Again, please edit the question.
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:44




















  • $begingroup$
    Use $pi$ for $pi$ and use $sqrt{wxyz}$ for $sqrt{wxyz}$.
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:41










  • $begingroup$
    This is called MathJax, a type of $LaTeX$. It works in the title section too.
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:42










  • $begingroup$
    Please edit the question accordingly :)
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:42










  • $begingroup$
    It might help to include what steps you took to get your answer, since what's important when studying Mathematics is not so much the answers to questions, but the reasons why they are the answers. Again, please edit the question.
    $endgroup$
    – Shaun
    Dec 8 '18 at 19:44


















$begingroup$
Use $pi$ for $pi$ and use $sqrt{wxyz}$ for $sqrt{wxyz}$.
$endgroup$
– Shaun
Dec 8 '18 at 19:41




$begingroup$
Use $pi$ for $pi$ and use $sqrt{wxyz}$ for $sqrt{wxyz}$.
$endgroup$
– Shaun
Dec 8 '18 at 19:41












$begingroup$
This is called MathJax, a type of $LaTeX$. It works in the title section too.
$endgroup$
– Shaun
Dec 8 '18 at 19:42




$begingroup$
This is called MathJax, a type of $LaTeX$. It works in the title section too.
$endgroup$
– Shaun
Dec 8 '18 at 19:42












$begingroup$
Please edit the question accordingly :)
$endgroup$
– Shaun
Dec 8 '18 at 19:42




$begingroup$
Please edit the question accordingly :)
$endgroup$
– Shaun
Dec 8 '18 at 19:42












$begingroup$
It might help to include what steps you took to get your answer, since what's important when studying Mathematics is not so much the answers to questions, but the reasons why they are the answers. Again, please edit the question.
$endgroup$
– Shaun
Dec 8 '18 at 19:44






$begingroup$
It might help to include what steps you took to get your answer, since what's important when studying Mathematics is not so much the answers to questions, but the reasons why they are the answers. Again, please edit the question.
$endgroup$
– Shaun
Dec 8 '18 at 19:44












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