SOLUTION: This question makes me crazy , please help me dear tutor . Find the height of a cylinder of maximum volume which can be cut from a cone of height 15cm and base radius 7.5cm .

Question 880998: This question makes me crazy , please help me dear tutor . Find the height of a cylinder of maximum volume which can be cut from a cone of height 15cm and base radius 7.5cm .
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
A linear relationship is between the cone's height above its base and the distance from center of the base. This slope is , or . You can view this slope as negative and form an equation .

What is the formula for VOLUME of the cylinder cut from this cone?
, x is the radius, y is the height. Having our formula, linear equation, for y means we can say:

An obvious restriction is to use only .
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 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.)
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