An open box is to be made from a rectangular piece of tin 12 inches long and 10 inches wide by cutting pieces of x-inch square from each corner and bending up the sides.

Question

a. Find a formula that expresses the volume V of the box as a function of x.
b. Find the domain of the function.

Answer 1

v(x) = x(12-2x)(10-2x)

Since the sides must have positive length, we need 10-2x > 0, or x<5

Since the cuts must also have nonzero length, x>0, so the domain is

0 < x < 5