Homework SourseA rectangular box with not top is to be constructed by cutti
A rectangular box with not top is to be constructed by cutting equal squares from each corner of a 4 ft by 4 ft rectangular piece of material and bending up the sides. Express the volume of the box as a function of its height. Then find the dimensions of the box that has maximum volume.
Solution
if x is the side of the square cut then height of the box will be x
now volume=l*b*h
l=b=4-2x
so volume=x(4-2x)^2
for max volume differentiate
you will get x=2,2/3
when x=2 volume is 0
so x=2/3
so maximum volume is 128/27 cubic feet
