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Subject: Re: How confident are you that you could have done this? (OT)

Author: F. Huber

Date: 11:25:08 02/14/06

On February 10, 2006 at 11:00:50, Derek Mauro wrote:

>The questions were supposedly given in order of difficulty.  I'll tell you the
>other 2 questions and you can judge for yourself.
>
>Question 4: An inverted cone is filled with water.  You are given 2 floating
>point numbers: the radius and height of the cone.  Find the radius of the sphere
>which if dropped into the cone would have caused the maxiumum amount of water to
>spill over the top.  The answer has to be accurate to 3 significant digits.

Here´s the solution for this puzzle:

With R and H being the radius and height of the cone, and to shorten the
solution

k = sqrt((H/R)^2+1) - 1

the optimum radius (r) of the sphere is:

r =  H*(k+1) / (k*(k+3))

and the maximum amount (V) of water spilled over the top:

V = 4*pi*H^3 / (3*k*(k+3)^2)

Of course my interpretation of the text above is, that this sphere has NOT to be
completely WITHIN the cone - otherwise there would be only one useful solution,
but _this_ sphere would not displace the most water!

Regards,
Franz.

• Re: How confident are you that you could have done this? (OT) Dann Corbit 13:23:40 02/14/06
  • Re: How confident are you that you could have done this? (OT) F. Huber 13:40:32 02/14/06
• Re: How confident are you that you could have done this? (OT) h.g.muller 12:16:55 02/14/06
  • Re: How confident are you that you could have done this? (OT) F. Huber 12:26:04 02/14/06
    • Re: How confident are you that you could have done this? (OT) h.g.muller 13:52:39 02/14/06
      • Re: How confident are you that you could have done this? (OT) John Merlino 16:09:01 02/14/06
        • Re: How confident are you that you could have done this? (OT) Derek Mauro 17:01:44 02/14/06

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