Question 880998
A linear relationship is between the cone's height above its base and the distance from center of the base.  This slope is {{{17/(7.5)}}}, or {{{34/15}}}.  You can view this slope as negative and form an equation {{{y=-(34/15)x+17}}}.


What is the formula for VOLUME of the cylinder cut from this cone?
{{{v=pi*x^2*y}}}, x is the radius, y is the height.  Having our formula, linear equation, for y means we can say:
{{{v=pi*x^2*(-(34/15)x+17)}}}
{{{v=pi*x^2(17-(34/15)x)}}}
{{{highlight(v=pi*17x^2-pi(34/15)x^3)}}}


An obvious restriction is to use only {{{0<x<7.5}}}.
This appears to be a derivative and function maximization exercise, but I'm stopping my part of the solution here.  You could also use a graphing calculator to look for the maximum value for v.


(Using Calculus, find {{{dv/dx}}} and equate to zero, solve for x.  Compute v that corresponds)

(Further note -  Actually, once you find x, you want to go to the formula for y to find the height where to cut the cone.)