Applied Max/Min Problems
Date: 2/11/96 at 14:48:46 From: J.Brian Casey Subject: Applied max/min problems Here's the question. Find the largest possible volume of a right circular cylinder that is inscribed in a sphere of radius r. All I know is that I have to differentiate the volume equation of the cylinder, but I don't know how to find my constant that I have to plug into the volume equation.
Date: 7/29/96 at 13:47:21 From: Doctor Alan Subject: Re: Applied max/min problems Hi Brian, The solution to your question can be answered by taking the following steps: 1. Set up your volume equation (for your cylinder) in terms of R (sphere) and the angle formed by R and the line perpendicular to h going through the center of the sphere. 2. Differentiate this with respect to theta (the angle). 3. Find the roots to the equation. There will be two roots. If you are using Mathematica, as I am, you may have to plot the derivative and choose the starting point for FindRoot command carefully. Note: By inspection of a sketch you will notice that theta must be between 0 and Pi/2. Good luck! -Doctor Alan, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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