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Math Help - Linear Equation

  1. #1
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    Linear Equation

    Having a bit of trouble with this one. Can anyone help?

    Many thanks.

    Q.
    The surface are, S, of a cylinder is given by S = 2 \pir2 + 2 \pirh. Its volume, V, is given by V = \pir2h. Express V in terms of S & r only.

    Attempt: V = S => \pir2h = 2 \pir2 + 2 \pirh => \pir2h = 2 \pi(r2 + rh) => V = ...

    Ans.: V = \frac{r}{2}(S - 2 \pir2)
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  2. #2
    Member sbhatnagar's Avatar
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    Re: Linear Equation

    S=2\pi r^2 + 2\pi r h
    \Rightarrow \pi r h = \frac{S}{2}-\pi r^2

    \therefore V= \pi r^2 h = (\pi r h)r=\left( \frac{S}{2}-\pi r^2 \right)r= \boxed{\frac{r}{2}\left( {S}-2\pi r^2 \right)}
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  3. #3
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    Re: Linear Equation

    Great. Thank you very much.
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  4. #4
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    Re: Linear Equation

    None of these equations are linear...
    Thanks from sbhatnagar
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