Thread: 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!!!

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".

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!!!

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?

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

n can be fraction