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A box has a volume of 48 cubic cm. A similiar box has volume of 6 cubic cm. what is the scale factor between each box?

  • math -

    (48/6)^(1/3)
    = 8^(1/3)
    = 2

    for example if a little cubical box had length 1 and a big one had length 2
    then the volume of the little one is 1^3 = 1
    and the volume of the big one is 2^3 = 8

    so a scale ratio of 2 leads to a volume ratio of 8

  • math -

    By the way, you happened to ask a ship designer.

  • math -

    thank you!

  • math -

    You are very welcome. I am used to model ships and the real things.

  • math -

    can prime other than 2and 5 3 apqrt
    explain

  • math -

    n and n+3
    If n is even (not prime), n+3 is odd
    If N is odd, n+3 is even (not prime)
    2 is the only even prime number, all bigger ones are divisible by 2.

  • math -

    damon i need to now where you got 1/3 from

  • math -

    (Vbig/Vsmall)^(1/3) is the cube root of the volume ratio

    the volume is proportional to the scale ratio cubed.

    If you have a scientific calculator
    try
    8^(1/3)
    and see if you get 2

    Most of us know by heart that 2^3 = 8 and 3^3 = 27 and 5^5 = 125

  • math -

    The 1/3 power comes from if A is the scale ratio
    then to get volume the x dimensions and the y dimensions and the z dimensions are all multiplied by A
    So the volume of the big one is A^3 times the volume of the little one.

  • math -

    thank you i get it now your awesome

  • math -

    You are very welcome.

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