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    Question 2 Page 150:

    A closed cylinder has total surface area equal to 600π. Show that the volume, Vcm3 , of this cylinder is given by the formula V=300πr – πr3, where r cm is the radius of the cylinder. Find the maximum volume of such a cylinder.


    Can someone help me with this - I am geting lost on the order in which to rearrange the equation for h...

    A = 2 pi rh + 2 pi r^2

    2 pi rh + 2 pi r^2 = 600 pi

    2pi (rh +r^2) = 600 pi

    rh +r^2 = 300 pi

    Now I am not sure if im on the right track OR where to go from here so I can substitute into the formula for the volume of a cylinder to get V=300πr – πr3

    I am getting really frustrated :-(

    Any step by step instructions would be great!
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    (Original post by christinajane)
    Question 2 Page 150:

    A closed cylinder has total surface area equal to 600π. Show that the volume, Vcm3 , of this cylinder is given by the formula V=300πr – πr3, where r cm is the radius of the cylinder. Find the maximum volume of such a cylinder.

    Can someone help me with this - I am geting lost on the order in which to rearrange the equation for h...

    A = 2 pi rh + 2 pi r^2

    2 pi rh + 2 pi r^2 = 600 pi

    2pi (rh +r^2) = 600 pi

    rh +r^2 = 300 pi

    Now I am not sure if im on the right track OR where to go from here so I can substitute into the formula for the volume of a cylinder to get V=300πr – πr3

    I am getting really frustrated :-(

    Any step by step instructions would be great!
    You know the formula for the volume is pi r^2 h.

    But the formula you're looking for doesn't contain h.

    So, rearrange the equation you've found to make h the subject and then substitute into the formula for the volume, eliminating h.
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    You're on the right track:

    Surface area is given by 2\pi r^2+2\pi rh=600\pi \Rightarrow r^2+rh=300.

    Now we don't want h, we only want things in terms of r, so solve for h: h=\dfrac{300-r^2}{r} and substitute into the formula for the volume V so that V=\pi r^2h=\pi r^2 \left(\dfrac{300-r^2}{r}\right)=\pi r(300-r^2)=300\pi r-\pi r^3, as required.
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    Let me know if you need help with the second part, but I think you'll be able to manage that .
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    (Original post by IrrationalRoot)
    Let me know if you need help with the second part, but I think you'll be able to manage that .

    Ahhh yes ok! I was getting stuck on how to get rid of the r in the denominator...below, I kept thinking I had to x by r to get rid of the denominator... or thinking that the r cancencelled out the r^2 above it :-(

    I always make silly mistakes like that - so basically the r in the denominator cancels out the r to the left of it??




    Yeah I can do the second bit think you - I was just geting frustrated because I couldn't understand how to get past that I posted earlier :-(
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    (Original post by christinajane)
    ...
    Yes \displaystyle r^2 \times \frac{a}{r} = \frac{r^2}{r} \times a = r^2 \times r^{-1} \times a = r^{2-1}  \times a = r \times a
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    (Original post by IrrationalRoot)
    Let me know if you need help with the second part, but I think you'll be able to manage that .
    Thank you very much by the way
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    (Original post by christinajane)
    Thank you very much by the way
    No problem .
 
 
 
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