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Posers and Puzzles

Posers and Puzzles

  1. Standard member talzamir
    Art, not a Toil
    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. Subscriber coquette
    Already mated
    25 Sep '11 17:59
    9 feet???
  3. Subscriber joe shmo On Vacation
    Strange Egg
    26 Sep '11 04:47
    I get the height to be

    100^(1/3)
  4. Subscriber joe shmo On Vacation
    Strange Egg
    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. Subscriber joe shmo On Vacation
    Strange Egg
    28 Sep '11 00:34
    Is your silence an indicator that I should try again?
  6. Standard member forkedknight
    Defend the Universe
    28 Sep '11 03:33 / 1 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 member talzamir
    Art, not a Toil
    28 Sep '11 07:19 / 1 edit
    Nice work. =)


    SOLUTION

    When the peak of the iceberg points down, the underwater

    part and the entire iceberg have the same shape.

    Let h be the height of the iceberg.

    Proportions in objects of the same shape are the same,

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

    which gives


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


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


    When the iceberg keels over, the part above water is of

    the same shape as the entire iceberg, with volume ratios

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


    (x : h)^3 = 1 : 10


    from which

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

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


    which is about 13 ft.