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Math Help - Mathematically similar...work out length

  1. #1
    Senior Member Mukilab's Avatar
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    Mathematically similar...work out length

    Two cylinders P and Q are mathematically similar.

    The total surface area of cylinder P is 90pi cm^2
    The total surface area of Cylinder Q is 810pi cm^2
    The length of cylinder P is 4cm

    Work out the length of cylinder Q


    Method NOT answer please
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  2. #2
    Senior Member Mukilab's Avatar
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    I'm guessing that it is 36.

    The surface area of Q divided by the surface area of P is 4. So I take P's length and times it by 4 giving me 36.

    I repeat this when it tells me to work out the volume. 100pi goes to 400pi. Or is it 100x4x4?
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  3. #3
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    Quote Originally Posted by Mukilab View Post
    Two cylinders P and Q are mathematically similar.

    The total surface area of cylinder P is 90pi cm^2
    The total surface area of Cylinder Q is 810pi cm^2
    The length of cylinder P is 4cm

    Work out the length of cylinder Q


    Method NOT answer please
    \dfrac{810}{90} = 9

    The area has increased 9 times.

    for a square:
    if you double the sides you get 4 times the area.
    if you triple the sides you get 9 times the area (see above)
    if you quadruple the sides you get 15 times the area.
    Two cylinders P and Q are mathematically similar.
    Since area is defined in square units, the length has increased by \sqrt{9} = 3

    If the length of cylinder P is 4 then the length of cylinder Q would be 4*3.

    You can compute the radius for cylinder P from the infomation given.
    Then multiply by 3 to get dimensions for cylinder Q.

    Does that make sense?

    .
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  4. #4
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    Quote Originally Posted by aidan View Post
    \dfrac{810}{90} = 9

    The area has increased 9 times.

    for a square:
    if you double the sides you get 4 times the area.
    if you triple the sides you get 9 times the area (see above)
    if you quadruple the sides you get 15 times the area.

    Since area is defined in square units, the length has increased by \sqrt{9} = 3
    Careful here! I and, I think, most people, would interpret "increased by 3" as meaning "+ 3". It would be better to say "multiplied by 3".

    [qote]If the length of cylinder P is 4 then the length of cylinder Q would be 4*3.

    You can compute the radius for cylinder P from the infomation given.
    Then multiply by 3 to get dimensions for cylinder Q.

    Does that make sense?

    .[/QUOTE]
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  5. #5
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    "Magnified by a factor of 3" would be acceptable language in this situation.
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  6. #6
    Senior Member Mukilab's Avatar
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    Thank you for the answers although I did understand by 3...
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