Math Is Fun Forum
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#1 2013-05-19 01:22:26
Maximise this!
Show that the height of a cylinder of maximum volume that can be inscribed in a sphere of radius R is
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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#2 2013-05-19 04:38:27
- {7/3}
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Re: Maximise this!
I have proved it,but i used calculus,do you want it?
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#3 2013-05-19 05:37:23
Re: Maximise this!
Yes, calculus would be fine
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#4 2013-05-19 07:56:23
- Bob
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Re: Maximise this!
hi Agnishom
The diagram below shows a cross section through the middle of the sphere (radius R).
The cylinder has radius r and height h.
You want the height for maximum V, so you need to differentiate and get dV/dh.
Where a formula has two variables (r and h) it is best to write one in terms of the other and substitute, to make a formula with only one variable.
By Pythag
So the volume can be written as
so
For a turning point this must be set to zero
But this does not yet show it is a maximum. It could, for example, be a minimum.
Differentiating again will sort this out. If the second derivative is negative, then it's a maximum.
For our 'h' this is clearly negative (don't need to get the exact value ... enough to find the sign), so the turning point is a maximum. 
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#5 2013-05-19 12:53:21
- {7/3}
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Re: Maximise this!
Hi,bob bundy,that's what i did too.
There are 10 kinds of people in the world,people who understand binary and people who don't.
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#6 2013-05-19 15:44:19
Re: Maximise this!
Got it 
Awesome Thanks bob bundy and {7/3}
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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