Dimensions of a Cardboard BoxDate: 09/28/97 at 14:37:01 From: Steve Subject: 9th grade Math.....Brain Twister A box with a square bottom and a volume of 2000 centimeters can be made by cutting 5-centimeter squares from the corners of a piece of cardboard and then turning up the sides. What should be the dimensions of the piece of cardboard? Please help - I am stumped. Date: 10/22/97 at 11:14:04 From: Doctor Mandel Subject: Re: 9th grade Math.....Brain Twister Dear Steve, You know that the sides of the box must be 5 cm high because the pieces you cut out of the flat board are 5 cm squares, so the walls are 5 cm tall. The volume of a box is equal to the area of the base times the height. Since you know the height and the volume of the box you can find out the area of the base. Just write out the equation: volume = (area of base)(height) and plug in a numbers you already know. Since you know that the base is a square you can find the length of one side of the base by finding the square root of the base's area. The length of the original side is the length of the base plus 10 cm, five on each side. Here's what the unfolded box would look like: |-5 CM--|--SIDE OF BOX--|-5 CM--| ------------------------------- - |XXXXXXX| |XXXXXXX| | |CUT OUT| |XXXXXXX| 5 CM |XXXXXXX| |XXXXXXX| | |-------|----FOLDS------|-------| - | | | | | | | | | | | | | | | | | | | | | | | | | | | | |-------|---------------|-------| |XXXXXXX| |XXXXXXX| |XXXXXXX| |XXXXXXX| |XXXXXXX| |XXXXXXX| ------------------------------- -Doctor Mandel, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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