Maximum Volume of a Box
Date: 04/13/97 at 02:18:47 From: Paul Subject: Maximum Volume of a Box Here's my question. It has me stumped. Please help and write back when you can. A rectangular sheet of cardboard measures 16cm by 6cm. Equal squares are cut out of each corner and the sides are turned up to form an open rectangular box. What is the maximum volume of the box? Thanks, Paul
Date: 04/13/97 at 06:44:13 From: Doctor Mitteldorf Subject: Re: Maximum Volume of a Box Dear Paul, Here's the most straightforward way to go about a problem like this: Notice that there's just one thing to play with, the size of the square. So let the length of a side of the square corner that's cut out be x. Then the base of the box that you get is (16-2x) * (6-2x) Now write a formula for the volume of the box in terms of x. Take that formula and differentiate it with respect to x. That shows how the volume changes when x is increased or decreased. Set that differentiated formula to equal zero. This is because if the differential were greater than 0, then you could increase x and get more volume; if it were less than 0, then you could decrease x and get more volume. Only if it's 0 is there no way to get more volume. After you've set the differentiated formula to equal zero, you have an equation in x which you can solve. Try this, and let me know if it works out for you. -Doctor Mitteldorf, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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