Question

Stephen has a set of plans to build a wooden box. He wants to reduce the volume of the box to 105 cubic inches. He would like to reduce the length of each dimension in the plan by the same amount. The plans call for the box to be 10 inches by 8 inches by 6 inches. Write and solve a polynomial equation to find out how much Stephen should take from each dimension.

Answer 1

First, please write out the formula for the volume of a box with rectangular base. V = ( ? ) * ( ? ) * (? )

Answer 2

...the general formula, that is.

Answer 3

I solved the brackets eve. I dont noe wat to do nxt..

Answer 4

the equation comes out to be xcubed -24xsquared +188x = 585

Answer 5

I'm sorry, but have no idea what you mean by "I solved the brackets eve." What were you trying to say?

If you're in either algebra or geometry, you've most probably already seen the formula for the volume of a rectangular box.

Answer 6

i solved the equation so far.... by multiplying the three brackets and then setting it equal to 105

Answer 7

I'd like to see how you got that. I'm asking you to begin with the formula for the volume of a rect. box.

Answer 8

sure pls

Answer 9

I was asking you for the GENERAL formula for the volume of that box. That formula is V = L*W*H, where L=length, W=width, and H=height.

What is the current volume of the box? (You're not asked for this, but I think the practice will benefit you.)

Answer 10

oh....
the left side of what i already wrote is the volume

Answer 11

xcubed -24xsquared +188x

Answer 12

I'm sorry, but we are not communicating very well. I've asked you to find the volume of the box with the given dimensions (before any dimension is reduced). Please do that.

Answer 13

okay it is 480

Answer 14

Yes, that's what I was asking for.

Now, we're going to need to shorten the width, length and height of the box by the same amount. Start with V = L * W * H and modify this formula to indicate that every dimension is now x units smaller than before. Write the new version of this volume formula.

Answer 15

(10 - x) * (8 - x) * (6 - x)

Answer 16

Right. That will give you the new volume of the box. What value should that new volume have?\

Answer 17

to answer that, please just copy what you've already written, above, and equate it to the new volume.

Answer 18

(10 - x) * (8 - x) * (6 - x) = 105

Answer 19

Very nice.

Now, hopefully, if you multiply out the left side and combine like terms, you should get the expression you shared with me before.

Answer 20

yes

Answer 21

What I would do would be to multiply the first 2 factors together. The result would then be 80-18x+x^2. Enclose that in parentheses and multiply this quantity by (6-x), please.

Answer 22

done

Answer 23

And your result is: ?

Answer 24

is it the equation i shared before.... xcubed -24xsquared +188x = 585

Answer 25

All right. I would have liked to have seen four terms on the left and 105 on the right.

But I'm going to assume that your result is correct. Why did you write '585' on the right side instead of on the left side?

Answer 26

umm......

Answer 27

what ans do u hav becauz mine is not correct i suppose

Answer 28

this is why I keep asking you to show your work. Only when I see your work can I give you meaningful feedback on what you've done.

Answer 29

I asked you to multiply (80-18x+x^2) by (6-x).

You should get FOUR terms. The constant term should be 480.

Would you do this multiplication now, please? Leave that '105' alone for now.

Answer 30

it comes out to be 480 - 188x + 24x^2 - x^3

Answer 31

I agree with you on this except for the x^2 term. Mind checking your work there? My result for that term is (-).

Answer 32

yeah

Answer 33

sorry to jst leave last time