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Math Help - Help !!! integration/differentiation

  1. #1
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    Exclamation Help !!! integration/differentiation


    Hey, thanks for looking.
    I have this q/
    A cylindrical tank, open at the top,has height hm and raduis rm.Its capacity is 1m^3.
    i) show that h=1/pie r^2. Which i did..1m^3=pie r^2 multiply by h, 1m^3-pie r^2=h, 1mpier^2=h, then finally 1/pier^2=h. Is this the correct workin?

    ii) Also, its total internal surface area is Sm^2. show that S=2/r +pier^2. Which iv done as,h multiplied by 2pier=2pie2h, pier^2+2pierh =pier^2+2pier.. but not sure where from here..

    iii) finally...Determine the value of r which makes the surface area S as small as possible..For this i need to make dy/dx and the 2nd diff, or integration..im not sure, either way could you show me as not sure how to do it with fractions..
    thank you
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  2. #2
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    Quote Originally Posted by Chez_ View Post

    Hey, thanks for looking.
    I have this q/
    A cylindrical tank, open at the top,has height hm and raduis rm.Its capacity is 1m^3.
    i) show that h=1/pie r^2. Which i did..1m^3=pie r^2 multiply by h, 1m^3-pie r^2=h, 1mpier^2=h, then finally 1/pier^2=h. Is this the correct workin?

    ii) Also, its total internal surface area is Sm^2. show that S=2/r +pier^2. Which iv done as,h multiplied by 2pier=2pie2h, pier^2+2pierh =pier^2+2pier.. but not sure where from here..

    iii) finally...Determine the value of r which makes the surface area S as small as possible..For this i need to make dy/dx and the 2nd diff, or integration..im not sure, either way could you show me as not sure how to do it with fractions..
    thank you
    For part 3, given S = \frac{2}{r} + \pi{r^2}, you want to minimize S. So we start by calculating dS/dr: \frac{dS}{dr} = -\frac{2}{r^2} + 2\pi{r}. So when is this equal to zero?
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  3. #3
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    so if this =o then i need to find what r=so i need to rearrange...
    How can this be re arranged to get r= ?
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  4. #4
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    Quote Originally Posted by Chez_ View Post
    so if this =o then i need to find what r=so i need to rearrange...
    How can this be re arranged to get r= ?
    Fairly easily:

    2\pi{r} = \frac{2}{r^2}

    \pi{r} = \frac{1}{r^2}

    \pi{r^3} = 1

    r^3 = \frac{1}{\pi}
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  5. #5
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    Following an eg, of 3-48/x^2=o ,48/x^2=3 then x^2=48/3 x=plus minus 4.....i did r^3=1/pie =0 , r=1/pie^3 but then it would be the third root of pie, which is 0.0322... but the answer sheet says r=0.683
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  6. #6
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    Quote Originally Posted by Chez_ View Post
    Following an eg, of 3-48/x^2=o ,48/x^2=3 then x^2=48/3 x=plus minus 4.....i did r^3=1/pie =0 , r=1/pie^3 but then it would be the third root of pie, which is 0.0322... but the answer sheet says r=0.683
    The third root of 1/pi is equal to \frac{1}{\pi^{1/3}}, not \frac{1}{\pi^3}. This might be where you are getting mixed up.
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  7. #7
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    Got it now, and understand where i went wrong!!
    THANK YOU!!
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