SOLUTION: Eliana wants to make a diorama for an art contest. She starts with a rectangular sheet of cardboard that is 12 in. long and 8 in. wide. She plans to make the diorama box by cutting
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-> SOLUTION: Eliana wants to make a diorama for an art contest. She starts with a rectangular sheet of cardboard that is 12 in. long and 8 in. wide. She plans to make the diorama box by cutting
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Question 1127225: Eliana wants to make a diorama for an art contest. She starts with a rectangular sheet of cardboard that is 12 in. long and 8 in. wide. She plans to make the diorama box by cutting identical squares from the corners and folding the sides to create a box with an open front, as shown below.
http://i66.tinypic.com/el4cjm.jpg
Eliana wants her diorama box to have the maximum allowable volume of 36 in ^3.
Determine all the possible lengths Eliana can use with the volume of 36 in ^3. Round dimensions to nearest hundredth of an inch.
In the diagram (http://i66.tinypic.com/el4cjm.jpg) x represents the side length of the squares Eliana will cut from each corner. Which dimension of the diormama box does x represent: the length or the width of the box, or the depth of the box from front to back?
You can put this solution on YOUR website! the volume is x (the height or depth)(12-2x)(8-2x)
that is 4x^3*40x^2+96x
and that equals 36
x=0.46 in and x=3 in
Lengths can be 6 inches (12-2(3)) and 11.08, with width 3 in
corresponding widths would be 2 and 7.08, with width 0.46 in
