Using differentials, estimate the amount of paint need to apply a coat of paint 2mm thick to a sphere with a...












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$begingroup$


So first I use the surface area of a sphere which is $$ SA=4pi r^2$$



but after that I have no idea what to do next because I shouldn't apply $frac{d}{dx}$ until I have substituted in something for $r$ right?










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  • 1




    $begingroup$
    Looks to me as if you're supposed to simplify $frac 43 pi (r+dr)^3 - frac 43 pi r^3$. And it simplifies to $4pi r^2 dr$.
    $endgroup$
    – I like Serena
    Dec 9 '18 at 1:09










  • $begingroup$
    @IlikeSerena. It does not simplify to that. It is approximated by that.
    $endgroup$
    – William Elliot
    Dec 9 '18 at 2:32
















0












$begingroup$


So first I use the surface area of a sphere which is $$ SA=4pi r^2$$



but after that I have no idea what to do next because I shouldn't apply $frac{d}{dx}$ until I have substituted in something for $r$ right?










share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    Looks to me as if you're supposed to simplify $frac 43 pi (r+dr)^3 - frac 43 pi r^3$. And it simplifies to $4pi r^2 dr$.
    $endgroup$
    – I like Serena
    Dec 9 '18 at 1:09










  • $begingroup$
    @IlikeSerena. It does not simplify to that. It is approximated by that.
    $endgroup$
    – William Elliot
    Dec 9 '18 at 2:32














0












0








0





$begingroup$


So first I use the surface area of a sphere which is $$ SA=4pi r^2$$



but after that I have no idea what to do next because I shouldn't apply $frac{d}{dx}$ until I have substituted in something for $r$ right?










share|cite|improve this question









$endgroup$




So first I use the surface area of a sphere which is $$ SA=4pi r^2$$



but after that I have no idea what to do next because I shouldn't apply $frac{d}{dx}$ until I have substituted in something for $r$ right?







calculus






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asked Dec 9 '18 at 1:00









Eric BrownEric Brown

737




737








  • 1




    $begingroup$
    Looks to me as if you're supposed to simplify $frac 43 pi (r+dr)^3 - frac 43 pi r^3$. And it simplifies to $4pi r^2 dr$.
    $endgroup$
    – I like Serena
    Dec 9 '18 at 1:09










  • $begingroup$
    @IlikeSerena. It does not simplify to that. It is approximated by that.
    $endgroup$
    – William Elliot
    Dec 9 '18 at 2:32














  • 1




    $begingroup$
    Looks to me as if you're supposed to simplify $frac 43 pi (r+dr)^3 - frac 43 pi r^3$. And it simplifies to $4pi r^2 dr$.
    $endgroup$
    – I like Serena
    Dec 9 '18 at 1:09










  • $begingroup$
    @IlikeSerena. It does not simplify to that. It is approximated by that.
    $endgroup$
    – William Elliot
    Dec 9 '18 at 2:32








1




1




$begingroup$
Looks to me as if you're supposed to simplify $frac 43 pi (r+dr)^3 - frac 43 pi r^3$. And it simplifies to $4pi r^2 dr$.
$endgroup$
– I like Serena
Dec 9 '18 at 1:09




$begingroup$
Looks to me as if you're supposed to simplify $frac 43 pi (r+dr)^3 - frac 43 pi r^3$. And it simplifies to $4pi r^2 dr$.
$endgroup$
– I like Serena
Dec 9 '18 at 1:09












$begingroup$
@IlikeSerena. It does not simplify to that. It is approximated by that.
$endgroup$
– William Elliot
Dec 9 '18 at 2:32




$begingroup$
@IlikeSerena. It does not simplify to that. It is approximated by that.
$endgroup$
– William Elliot
Dec 9 '18 at 2:32










1 Answer
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$begingroup$

$V = 4/3×pi r^3$
$dV/dr = 4pi r^2$

Lower estimate for paint volume is
$dV = 4pi r^2 dr$



dr = 2mm, r = 30cm. Calculate dV in cm$^3.$






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    1 Answer
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    1 Answer
    1






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    0












    $begingroup$

    $V = 4/3×pi r^3$
    $dV/dr = 4pi r^2$

    Lower estimate for paint volume is
    $dV = 4pi r^2 dr$



    dr = 2mm, r = 30cm. Calculate dV in cm$^3.$






    share|cite|improve this answer









    $endgroup$


















      0












      $begingroup$

      $V = 4/3×pi r^3$
      $dV/dr = 4pi r^2$

      Lower estimate for paint volume is
      $dV = 4pi r^2 dr$



      dr = 2mm, r = 30cm. Calculate dV in cm$^3.$






      share|cite|improve this answer









      $endgroup$
















        0












        0








        0





        $begingroup$

        $V = 4/3×pi r^3$
        $dV/dr = 4pi r^2$

        Lower estimate for paint volume is
        $dV = 4pi r^2 dr$



        dr = 2mm, r = 30cm. Calculate dV in cm$^3.$






        share|cite|improve this answer









        $endgroup$



        $V = 4/3×pi r^3$
        $dV/dr = 4pi r^2$

        Lower estimate for paint volume is
        $dV = 4pi r^2 dr$



        dr = 2mm, r = 30cm. Calculate dV in cm$^3.$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 9 '18 at 2:52









        William ElliotWilliam Elliot

        7,6072720




        7,6072720






























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