A box is to be made out of a 6 cm by 20 cm piece of cardboard. Squares of side length x cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.
Express the volume V of the box as a function of x.
Give the domain of V in interval notation. (Use the fact that length, width, and volume must be positive.)
Find the length L, width W, and height H of the resulting box that maximizes the volume. (Assume that W ≤ L)
L = cm
W = cm
H = cm
The maximum volume of the box is cm3.