Math Is Fun Forum

gourish

Member

Registered: 2013-05-28

Posts: 153

functions #2 related to geometry

a cylinder is inscribed in a sphere of radius R. the volume V of the cylinder is written as V=f(x) where x is the height of the cylinder
find the function with it's domain and range. when is it maximum and when is it minimum?

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"The man was just too bored so he invented maths for fun"
-some wise guy

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: functions #2 related to geometry

hi gourish,

Once again, I've made a diagram with the height 'on its side' so that x is across.

If the cylinder is height x, then the centre of the sphere is at (½x,0) and you can use Pythagoras to get y, the radius of the cylinder, in terms of x and R.  Is that enough to get you to an answer?

Bob

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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

gourish

Member

Registered: 2013-05-28

Posts: 153

Re: functions #2 related to geometry

thanks again bob you make them look so simple with the diagrams.

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"The man was just too bored so he invented maths for fun"
-some wise guy