Esther Tan

Posted on Monday, 24 February, 2003 - 04:23 pm:

I can't seem to be able to solve this supposedly simple GCSE question. (how embarrassing!)

A cylinder of volume V is to be cut from a sphere of radius r. What is the maximum volume of the cylinder?

I think i'm having a mental block. i know what to do after i express h (the height of the cylinder) in terms of R (the radius of the cylinder). please help!
Thanks in advance!

esther

Yatir Halevi

Posted on Monday, 24 February, 2003 - 05:21 pm:

The volume of a cylinder is

2 π R h

(where

R

is radius of the cylinder). Now we need a way to express

R

h

and

r

. Try imagining the sphere and the clyinder inside it. Connect the center point of the sphere with the centre of the base of the cylinder call this

h / 2

, now connect it also with the edge of the base (with the circle itself). Can you see how to continue from here?
Write back if you need another hint.

Yatir

Esther Tan

Posted on Monday, 24 February, 2003 - 05:45 pm:

Thanks a lot Yatir!

The volume of a cylinder is actually $π R^{2} h$ but don't worry, i managed to get the answer :)
The pythagoras part didn't strike me at first and i tried to use proportion. Thank you for your help!

esther

Yatir Halevi

Posted on Monday, 24 February, 2003 - 06:02 pm:

You welcome! (Of course I meant that...)

Yatir