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Math Help - Cylinder exterior surface area

  1. #1
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    Cylinder exterior surface area

    Hi guys,

    ive been given the question; a container made from thin metal is in the shape of a right circular cylinder with a height h cm and a base radius r cm. the container has no lid. When full of water, the container holds 500cm3 of water.

    show that the exterior surface area, A cm2, of the container his given by;

    A=(pi)r^2 + 1000/r

    Can anybody guide me on how to tackle this problem please? Should I transpose the formula and substitute A for 500cm3 to begin with?

    thanks,

    Kris
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  2. #2
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    Re: Cylinder exterior surface area

    Hey Krislton.

    What are your formulas for the volume of a cylinder and the area of a cylinder?

    Hint: The area of a cylinder (with no top) is the surface area of the cylinder and the bottom (remember circumferences for the cylinder) and the volume of a cylinder and see how to use the information in the volume to simplify the expression for the area.

    You have two variables in these: r and h so you will get rid of at least one of them.
    Thanks from Krislton
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  3. #3
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    Re: Cylinder exterior surface area

    Thanks for the input. Too be honest I didn't know the formula for a cylinder surface area but you definitely put me on track.

    So to show this I worked out that by transposing (pi)r^2h was the first formula, h=500/(pi)r^2 which meant I could then insert that in the formula which enabled me to show the given formula was correct.

    Thanks,

    Kris
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  4. #4
    Junior Member alane1994's Avatar
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    Re: Cylinder exterior surface area

    Formula for surface area of a cylinder.

    A=2\pi r h+2\pi r^2

    But you only have one end of the cylinder, so you can get rid of one end of it.

    A=2\pi r h+\pi r^2

    You want to get this right?

    A=\pi r^2 +\frac{1000}{r}

    Formula for volume of a cylinder.

    V=\pi r^2 h

    From there I would solve the volume formula for h, and put it into the area formula. From there, simplify and see what happens. I may be wrong, someone correct me if that turns out to be the case.
    Last edited by alane1994; October 11th 2012 at 11:40 AM. Reason: Latex Errors
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  5. #5
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    Re: Cylinder exterior surface area

    Yep you are correct, thanks
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