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Posers and Puzzles
60.13N / 25.01E
Joined 19 Sep '11 Moves 56935 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?
Omaha, Nebraska, USA
Joined 04 Jul '06 Moves 1114597 R
Removed
Joined 10 Dec '06 Moves 8528 I get the height to be
100^(1/3)
R
Removed
Joined 10 Dec '06 Moves 8528 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
R
Removed
Joined 10 Dec '06 Moves 8528 Is your silence an indicator that I should try again?
127.0.0.1
Joined 18 Dec '03 Moves 16687 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
60.13N / 25.01E
Joined 19 Sep '11 Moves 56935 Nice work. =)
SOLUTION
Reveal Hidden ContentWhen the peak of the iceberg points down, the underwater
Reveal Hidden Contentpart and the entire iceberg have the same shape.
Reveal Hidden ContentLet h be the height of the iceberg.
Reveal Hidden ContentProportions in objects of the same shape are the same,
Reveal Hidden Contentexcept that they are squared for areas and cubed for volumes,
Reveal Hidden Contentwhich gives
Reveal Hidden Content((h-1) : h)^3 = 9 : 10
Reveal Hidden Contentfrom which h = 1 ft / (1 - (9 : 10)^(1/3)) , or about 29 feet.
Reveal Hidden ContentWhen the iceberg keels over, the part above water is of
Reveal Hidden Contentthe same shape as the entire iceberg, with volume ratios
Reveal Hidden Content1 : 10. Let x be the height of the visible part of the iceberg.
Reveal Hidden Content(x : h)^3 = 1 : 10
Reveal Hidden Contentfrom which
Reveal Hidden Contentx = (1 : 10)^(1/3) h
Reveal Hidden Contentx = 1 ft * (1 : 10)^(1/3) / (1 - (9 : 10)^(1/3))
Reveal Hidden Contentwhich is about 13 ft.
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