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janky
07-17-2011, 05:47 PM
The question I'm stuck on asks:
"An open-top box with a square base is to be constructed using 120 square centimeters of material. What dimensions will produce a box:
a) of volume 100 cubic centimeters
b) with largest possible volume?"

I know area = l*w
and volume = l*w*h

I'm assuming I'll have to get two equations w variables, solve for one variable, substitute it back in, get a quadratic, then graph/solve.

I have no idea where to even begin :(

please help?

Subhotosh Khan
07-17-2011, 06:45 PM
The question I'm stuck on asks:
"An open-top box with a square base is to be constructed using 120 square centimeters of material. What dimensions will produce a box:
a) of volume 100 cubic centimeters
b) with largest possible volume?"

I know area = l*w
and volume = l*w*h

I'm assuming I'll have to get two equations w variables, solve for one variable, substitute it back in, get a quadratic, then graph/solve.

I have no idea where to even begin :(

please help?

Assuming the box has dimensions x, x & h - what is the external surface area of your "open top box"?

Remember that your box is made out of 4 rectangles and one square.

Denis
07-19-2011, 08:28 PM
Here's a case where Volume = Area:
square sides = x = 8, height = h = 2 :
Volume = x * x * h = 8 * 8 * 2 = 128
Area = x * x + 4 * x * h = 8 * 8 + 4 * 8 * 2 = 128

Hope that'll make it easier for you to "see"....

Btw, are you sure the area in your problem is 120, not 125?