# Thread: finding the volume and the domain of an open box

1. ## finding the volume and the domain of an open box

An open box is to be made from a flat square piece of material 18 inches in length and width by cutting equal squares of length from the corners and folding up the sides.
Write the volume 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=

If we write the domain of the box as an open interval in the form (a,b) , then what is a? b?

2. Originally Posted by rosco
An open box is to be made from a flat square piece of material 18 inches in length and width by cutting equal squares of length from the corners and folding up the sides.
Write the volume 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=

If we write the domain of the box as an open interval in the form (a,b) , then what is a? b?

well, since this will obviously count towards your grade, we can't give you answers. see post #2 here: http://www.mathhelpforum.com/math-he...-problem2.html

3. Originally Posted by rosco
An open box is to be made from a flat square piece of material 18 inches in length and width by cutting equal squares of length from the corners and folding up the sides. Write the volume of the box as a function of x. Leave it as a product of factors; you do not have to multiply out the factors.
Draw the square, and label the sides with the given dimension. Draw the squares cut from the corners, and label the sides with the given variable.

Dash in lines for where you'll be folding up the sides.

Using the given dimension and the given variable, create an expression for the dimensions of the base of the box, given that you'll be folding up a width of "x" units on each side.

Obviously the height of the box is "x". What expressions represent the other two dimensions? Multiply the variable and the expressions to find the volume V in terms of the variable.

Originally Posted by rosco
If we write the domain of the box as an open interval in the form (a,b) , then what is a? b?
Boxes, being physical objects, cannot have zero or negative dimensions. Use this fact to find the limits on the realistic values of x.

Have fun!