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 .

Algebra ->  Volume -> 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 .      Log On


   

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) About Me  (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 17%2F%287.5%29, or 34%2F15. You can view this slope as negative and form an equation y=-%2834%2F15%29x%2B17.

What is the formula for VOLUME of the cylinder cut from this cone?
v=pi%2Ax%5E2%2Ay, x is the radius, y is the height. Having our formula, linear equation, for y means we can say:
v=pi%2Ax%5E2%2A%28-%2834%2F15%29x%2B17%29
v=pi%2Ax%5E2%2817-%2834%2F15%29x%29
highlight%28v=pi%2A17x%5E2-pi%2834%2F15%29x%5E3%29

An obvious restriction is to use only 0%3Cx%3C7.5.
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%2Fdx 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.)