maximum volume question math
A shadow box is a type of picture frame that allows you to put your treasures on display. It is an open box with a glass lid that can stand on a table or be hung from a wall. Determine the maximum volume a shadow box can have if it is to be made from a rectangular piece of cardboard with dimensions 22 inches by 16 inches.
really confused on how to start this question, im assuming I need to use the formula V=WxHxL but inorder to do that I would need a third measurement
any help is appreciated, Im not asking you to do this question for me just asking what I need to do inorder to solve. THANKS!
March 11, 2015
3 Comments • Newest first
Is the cardboard rectangle supposed to make up one side of the box or is that what the cutouts for the box will be made of?
x * (22-2x) * (16-2x)
Your interval: [0,8] (x must be between these numbers or else problem is going to be wonky)
If you need that in multiplied out form:
[352x - 76(x^2) + 4(x^3)]
1st x is your height
2nd 22-2x is your length, two square cut outs on the 22 side.
3rd 16-2x is your width, two square cut outs on the 16 side.
It is -2x because you're cutting out 2 sides of unknown length and width.
You're multiplying an extra x because when you fold up the sides, the x you cut out is the height of the box.
everyone knows you just multiply the dimensions to find volume. you coward