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

- Thread starter misstina
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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

- Joined
- Apr 12, 2005

- Messages
- 9,791

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?

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......

- Joined
- Apr 12, 2005

- Messages
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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

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.

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?