Posers and Puzzles

Posers and Puzzles

  1. Standard membertalzamir
    Art, not a Toil
    60.13N / 25.01E
    Joined
    19 Sep '11
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    46203
    24 Sep '11 23:54
    An iceberg floats in water so that 90% of its volume is underwater. The iceberg is shaped like a cone, with peak pointing down, base up, and the base rises one foot above the surface of the water. If the iceberg tilts so that base is down and peak up, how high from the water surface will the peak rise?
  2. Subscribercoquette
    Already mated
    Omaha, Nebraska, USA
    Joined
    04 Jul '06
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    957031
    25 Sep '11 17:59
    9 feet???
  3. Subscriberjoe shmo
    Strange Egg
    podunk, PA
    Joined
    10 Dec '06
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    7733
    26 Sep '11 04:47
    I get the height to be

    100^(1/3)
  4. Subscriberjoe shmo
    Strange Egg
    podunk, PA
    Joined
    10 Dec '06
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    7733
    27 Sep '11 03:02
    Originally posted by joe shmo
    I get the height to be

    100^(1/3)
    nevermind, thats not correct...looks a bit more complicated at this time of day.

    my latest result is

    approx

    13.45 ft
  5. Subscriberjoe shmo
    Strange Egg
    podunk, PA
    Joined
    10 Dec '06
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    7733
    28 Sep '11 00:34
    Is your silence an indicator that I should try again?
  6. Standard memberforkedknight
    Defend the Universe
    127.0.0.1
    Joined
    18 Dec '03
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    16172
    28 Sep '11 03:331 edit
    Originally posted by joe shmo
    nevermind, thats not correct...looks a bit more complicated at this time of day.

    my latest result is

    approx

    13.45 ft
    This is what i get.

    The total height of the cone is
    H = 10 + 3 * 30^(1/3) + 30^(2/3) ~= 28.977
  7. Standard membertalzamir
    Art, not a Toil
    60.13N / 25.01E
    Joined
    19 Sep '11
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    46203
    28 Sep '11 07:191 edit
    Nice work. =)


    SOLUTION

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    When the peak of the iceberg points down, the underwater

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    part and the entire iceberg have the same shape.

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    Let h be the height of the iceberg.

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    Proportions in objects of the same shape are the same,

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    except that they are squared for areas and cubed for volumes,

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    which gives


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    ((h-1) : h)^3 = 9 : 10


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    from which h = 1 ft / (1 - (9 : 10)^(1/3)) , or about 29 feet.


    Reveal Hidden Content
    When the iceberg keels over, the part above water is of

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    the same shape as the entire iceberg, with volume ratios

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    1 : 10. Let x be the height of the visible part of the iceberg.


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    (x : h)^3 = 1 : 10


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    from which

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    x = (1 : 10)^(1/3) h

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    x = 1 ft * (1 : 10)^(1/3) / (1 - (9 : 10)^(1/3))


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    which is about 13 ft.
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