cuboid of maximum volume

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

cuboid of maximum volume

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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Source: Beat The GMAT — Problem Solving | Thu Apr 02, 2009 5:22 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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