Question

A cylinder is inscribed in a right circular cone of height 5.5 and radius (at the base) equal to 4.5. What are the dimensions of such a cylinder which has maximum volume?

Answer 1

Let h be the height of the cylinder and let r be its radius.
Slice =:
(5.5-h)/5.5 = r/4.5
9(11/2 - h) = 11r
h = 11(1/2-r/9)

We want to maximize πr²h so take a derivative and set it equal to 0:
d(11πr²(1/2-r/9))/dr = 11π(r-r²/3) = 0
So r = 0 or 3, and clearly 0 won't give a maximum, so we'll go with
r=3 => h=11/6

Answer 2

sorry but this may seem like a dumb question, but how do you know when you need to take the derivative of something? or is it just maximizing questions in general?

Answer 3

To find the maximum or minimum you will need to take the derivative.

Answer 4

alright! thanks a lot!! :)