SOLUTION: You cut square corners from a piece of cardboard that has dimensions 32 cm by 40 cm. You then fold the cardboard to create a box with no lid. To the nearest centimeter, what are th

Algebra ->  Volume -> SOLUTION: You cut square corners from a piece of cardboard that has dimensions 32 cm by 40 cm. You then fold the cardboard to create a box with no lid. To the nearest centimeter, what are th      Log On


   

Question 739455: You cut square corners from a piece of cardboard that has dimensions 32 cm by 40 cm. You then fold the cardboard to create a box with no lid. To the nearest centimeter, what are the dimensions of the box that will have the greatest volume?

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
volume, v = area of bottom multiplied by height of each side.
x=height of each side, from cutting out the corners.

two sides are 32-2x, and other two sides are 40-2x lengths.
They make the bottom area.

v = height * oneSideLength * otherSideLength
v=x%2832-2x%29%2840-2x%29
highlight%28v=4x%2816-x%29%2820-x%29%29
OR
highlight%28v=4x%5E3-144x%5E2%2B1280x%29.

You would either use a graphing calculator to find the maximum, or resort to Calculus taking derivative to find the maximum.
dv%2Fdx+=+12x%5E2-288x%2B1280+
Find where 12x%5E2-288x%2B1280+=0.