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Math Help - What radius would equal 24(pi) times this radius?

  1. #1
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    What radius would equal 24(pi) times this radius?

    For my algebra class, this is the only question im stuck on this section:

    Grain silos can be described as a hemisphere sitting atop a cylinder. The interior volume V of the silo can be modeled by V = 2/3(pi)r3 + (pi)r2h Where h=height of a cylinder with radius r. For a cylinder 6m tall, what radius would give the silo a volume that is numerically equal to 24(pi) times this radius?

    That's the problem, word-for-word verbatim. 2/3 is a fraction and pi is the symbol for (pi). I'm lost How do I use the Latex thing so I can type it out exactly as it appears?

    Any help would be greatly appreciated.
    Last edited by Rtedmonston; September 1st 2012 at 09:35 AM.
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  2. #2
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    Re: What radius would equal 24(pi) times this radius?

    Quote Originally Posted by Rtedmonston View Post
    For my algebra class, this is the only question im stuck on this section:

    Grain silos can be described as a hemisphere sitting atop a cylinder. The interior volume V of the silo can be modeled by V = 2/3(pi)r3 + (pi)r2h Where h=height of a cylinder with radius r. For a cylinder 6m tall, what radius would give the silo a volume that is numerically equal to 24(pi) times this radius?

    That's the problem, word-for-word verbatim. 2/3 is a fraction and pi is the symbol for (pi). I'm lost How do I use the Latex thing so I can type it out exactly as it appears?

    Any help would be greatly appreciated.
    You only have to "translate" the text into an equation:

    \frac23 \pi r^3+\pi \cdot r^2 \cdot h = 24 \pi \cdot r

    Replace h by 6:

    \frac23 \pi r^3+6 \pi \cdot r^2  = 24 \pi \cdot r

    Collect all terms on the LHS and factor out \pi r :

    \pi r \left( \frac23  r^2+6  \cdot r  - 24  \right)=0

    A product of 2 factors equals zero if at least one factor equals zero. By the 1st factor you'll get r = 0 which is a very, very slim cylinder, nearly invisible

    With the 2nd factor you have to solve a quadratic equation in r:

    \frac23  r^2+6  \cdot r  - 24 = 0

    You'll get 2 solutions for r. The negative value isn't very plausible here.
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