# [MOVED] Word Problem: An open-top box is to be constructed

#### misstina

##### New member
An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.

Find the function V that represents the volume of the box in terms of x.

I seem to get lost in translating what equation they are looking for, can someone please help.

thank you
misstina

#### tkhunny

##### Moderator
Staff member
Did you draw a picture? It's just a rectangle with squares cut out of the corners.

Grab a piece of paper and fold up the sides. Get a vision of it.

x is in feet. If it's 6 inches, that would be x = 1/2.

Original 6 ft by 8 ft

Base after folding up flaps.

(6 - 2x) ft by (8 - 2x) ft

That's the base. What's the height? That's all you need for the volume.

Bonus Question: x MUST be less than 3 ft. Why?
Bonus Question: x MUST be greater than 0 feet. Why?

#### misstina

##### New member
honestly, I feel very stupid. I can see where two sides would be 6 ft - 2(2 corners) and the other two sides would be 8 ft - 2(2 corners).

but outside of that im completely lost, i keep reading this over and over again, but it escapes me.

the volume I would think would be 6^2 + 8^2 = 36 + 64 = 100
but to figure out the amount cut......

#### tkhunny

##### Moderator
Staff member
No feeling stupid. We don't allow that, here. :wink: This is where you have to lean back and take a deep breath.

You have just written some nonsense. You cannot possibly believe that multiplying TWO numbers will give you a VOLUME. That would be only AREA. You know that, don't you? Never do that again!

Width: (6 - 2x) ft
Length: (8 - 2x) ft
Height: x ft

Volume = Width*Length*Height = (6 - 2x) ft * (8 - 2x) ft * (x ft)

Now what? Read the problem statement again. What does it want?

One step at a time. No need to panic.

#### misstina

##### New member
it doesn't seem to want a solution, just the equation for finding the volume. Correct?

#### Denis

##### Senior Member
Correct Miss Tina; just multiply out what TK gave you:
V = x(6 - 2x)(8 - 2x)
V = 4x^3 - 28x^2 + 48x

Try it out; make x = 2; you'll get V = 16

And if you do cut off 2by2 squares at the corners of the 6by8,
then fold up to form the box, the box is 2by2by4, right?
And 2 * 2 * 4 = 16 : capish?

#### misstina

##### New member
Thank you so much. I was loosing my mind on this.