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If eacj dimension of a box is quadrupled, how are the surface area and the volume affected?

  • Geometry -

    I'll do volume to show you

    V = L*w*h
    1st example, L = 2, w = 3, h = 4
    V = 2*3*4
    V = 24

    Quadruple each dimension,
    L = 2*4 = 8, w = 3*4 = 12, h = 4*4 = 16
    V = 8*12*16
    V = 1536

    So, the volume went from 24 to 1536
    1536/24 = 64 so 24*64 = 1536

    So, if you quadruple the dimensions, the volume is increased 64 times

    Follow this for the Area
    here is the formula
    TA = 2Lw + 2Lh + 2wh

  • Geometry -

    which one is length width height

  • Geometry -

    I don't understand what you are asking
    use this formula
    TA = 2Lw + 2Lh + 2wh
    use these dimensions
    1st use, L = 2, w = 3, h = 4

    then quadruple the dimensions to compare how the area changed
    2nd use L = 8, w = 12, h = 16 (I quadrupled the dimensions for you)

    you can use any dimensions you want, I just gave you dimensions for example

  • Geometry -

    length = L
    width = W
    height = H
    V = LWH
    SA = 2(LW + LH + WH)

    new one:
    length = 4L
    width = 4W
    height = 4H

    volume = (4L)(4W)(4H)
    = 64 LWH

    so the volume is 64 times as large, helper had that also.

    SA = 2(16LW + 16LH + 16WH)
    = 32(LW + LH + WH)

    so the surface area is 32 times as large.

  • Geometry -

    I can't believe I didn't think to do it your way!!!

    so much easier to do AND understand

    that's why you are the tutor
    thank you

    I've learned so much from your posts! I wish I had you to ask questions when I was taking math.

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