Help differential problem (application)

• Jul 29th 2012, 02:51 PM
oponion
Help differential problem (application)
the maximum volume enclosed by circular cylinder inscribed in a sphere equal to n times the volume of the sphere, find the value of n
how to solve this??

i know using the pyth theorem , the square of radius of cylinder + 1/2 square of the height of the cylinder is equal to square of the sphere's radius
i also list two volume equations

but how to do the next step???

because there are two variable, it seems cannot be reduced to only 1 variables

HELP!!!
• Jul 29th 2012, 05:45 PM
HallsofIvy
Re: Help differential problem (application)
Quote:

Originally Posted by oponion
the maximum volume enclosed by circular cylinder inscribed in a sphere equal to n times the volume of the sphere, find the value of n

I don't know what you mean here. First there should be a verb in the first clause. If you meant the volume of the cylinder is "equal to n times the volume of the sphere", that's impossible. The volume of a cylinder inscribed in a sphere must be less than then volume of the sphere, not "n times the volume".

Quote:

how to solve this??

i know using the pyth theorem , the square of radius of cylinder + 1/2 square of the height of the cylinder is equal to square of the sphere's radius
i also list two volume equations

but how to do the next step???

because there are two variable, it seems cannot be reduced to only 1 variables

HELP!!!
• Jul 29th 2012, 07:18 PM
Prove It
Re: Help differential problem (application)
Quote:

Originally Posted by HallsofIvy
I don't know what you mean here. First there should be a verb in the first clause. If you meant the volume of the cylinder is "equal to n times the volume of the sphere", that's impossible. The volume of a cylinder inscribed in a sphere must be less than then volume of the sphere, not "n times the volume".

Couldn't you have n be a fraction?
• Jul 29th 2012, 07:57 PM
oponion
Re: Help differential problem (application)
sorry, i missed some verbs

the problem is the maximum volume enclosed by a circular cylinder inscribed in a sphere equals n times the volume of the sphere. find k

yes...n can be any real number
• Jul 29th 2012, 07:58 PM
oponion
Re: Help differential problem (application)
n can be fraction