An open box is to be made from a flat square piece of material 20 inches in length and width by cutting equal squares of length x from the corners and folding up the sides.

Question

(a) Write the volume V of the box as a function of x. Leave it as a product of factors; you do not have to multiply out the factors.

V(x)=

(b) Give the domain of this volume function in interval notation:

Answer 1

base will be 20-2x by 20-2x, and the height will be x
Volume = x(20-2x)(20-2x) or x(20-2x)^2

clearly each of the dimensions must be positive, so 20-2x > 0
-2x > -20
x < 10

In my notation, 0 < x < 10, I will let you change it to yours.