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cuboid of maximum volume

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by sanju09 » Thu Apr 02, 2009 5:22 am
A square piece of cardboard of side 20 is taken and four equal small squares are removed from the corners. The sides are then turned up to make a cuboid of maximum volume. What would be the dimensions of such a cuboid?
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Re: cuboid of maximum volume

by Brent@GMATPrepNow » Fri Apr 03, 2009 6:28 am
sanju09 wrote:A square piece of cardboard of side 20 is taken and four equal small squares are removed from the corners. The sides are then turned up to make a cuboid of maximum volume. What would be the dimensions of such a cuboid?
This question is a classic question in differential calculus.
1) Let x be the length of one side of the removed square.
2) Create a volume function in terms of x
3) Find the derivative of the function
4) Find the value of x for which the derivative equals 0.
.
.
.
Wait a second . . . find the derivative?
As you might guess, this is definitely not a GMAT question. However, if you're studying for a Calculus 101 test, then you better know how to solve max/min problems.
Brent Hanneson - Creator of GMATPrepNow.com
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