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Math Help - How do i solve ?

  1. #1
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    How do i solve ?

    I need to calculate the diameter of a cylinder . However the cylinder has a hemisphere as a lid and a flat bottom.
    I am given the overall surface area which is 2M square
    The overall height is 84cm. Thats it

    I can formulate the cylinder diameter if it didn't have a hemisphere top using quadratics however i just cant see how to get this.

    SA of hemisphere = 2 pi r square
    Sa of base = 1 Pi r square
    Cylinder height H= h - r
    Cylinder area = 2 pi r H

    any help please.....
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  2. #2
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    Re: How do i solve ?

    how much height does the hemisphere add to the cylinder? That should remove one of your variables up there.
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  3. #3
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    Re: How do i solve ?

    it removes the radius from the height and thats my problem i dont know the radius. with out the hemispere its around 3.6 ...
    .Total SA ( 2 M sq ) = 3 pi r sq + 2 pi r (.84m)-r ) solve for r ?

    can i remove r from + 2 pi r ( .84 - r ) so that its just + 2 pi ( .84) by cancelling ?
    Last edited by civil; December 11th 2013 at 12:38 AM.
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  4. #4
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    Re: How do i solve ?

    yep
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  5. #5
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    Re: How do i solve ?

    So my formula would be SA ( 2m sq ) = 3 pi r Sq + 2 pi (.84 ) ?
    Last edited by civil; December 11th 2013 at 01:31 AM.
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  6. #6
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    Re: How do i solve ?

    no...

    it's 2 pi r (0.84) - pi r2 = 2

    you cancel the pi r2 terms

    incidentally... it's not pi r sq. it's either pi r^2, or pi r2, or even \pi r^2
    Last edited by romsek; December 11th 2013 at 12:54 AM.
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  7. #7
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    Re: How do i solve ?

    please see attachment ......
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  8. #8
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    Re: How do i solve ?

    I see a couple problems.

    First 2 sq. M is 20,000 sq. cm.

    But a more serious problem is that you have SA = 3\pi r^2 + 2 \pi r (84)

    That's not correct. The entire solid is 84 cm. The cylinder is 84-r cm

    so SA = 3\pi r^2 + 2 \pi r (84-r)

    fix these and resolve it and you should be good to go.
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  9. #9
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    Re: How do i solve ?

    Think this is right now ....cheers for you help and let us know if you agree ?
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  10. #10
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    Re: How do i solve ?

    think this ones right ...?
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  11. #11
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    Re: How do i solve ?

    Quote Originally Posted by civil View Post
    think this ones right ...?
    I don't really understand why all the trouble with algebra. I'm going to work in meters.

    Total height is L, the cylinder height is (L-r)

    SA = \pi r^2 + 2 \pi r^2 + 2 \pi r (L-r)

    SA =  3 \pi r^2 + 2 \pi r (L-r)

    SA = 3 \pi r^2 + 2 \pi r L - 2 \pi r^2 = \pi r^2 + 2 \pi r L

    \pi r^2 + 2 \pi r L - 2 = 0

    \pi r^2 + 2 \pi r (0.84) - 2 = 0

    \pi r^2 + (1.68) \pi r - 2 = 0

    r=0.318542 m

    There is a negative root as well but radii can't be negative.
    Last edited by romsek; December 11th 2013 at 10:26 AM.
    Thanks from civil
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  12. #12
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    Re: How do i solve ?

    cant believe ive been so f!"$ing blind/stupid/blond cheers for help..... just out of interest why did the quadratic work when wrong ?
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