# Calculating the cut out section of a box

#### Emethyst

1. Homework Statement
a rectangular box with no top is formed by cutting out equal squares from the corners of a square sheet of metal, 10 cm by 10cm, and bending up the 4 sides. What size of square must be removed from each corner to generate a box with a volume of 50cm^3? (Note: there are 2 answers.)

2. Homework Equations
Tangent Line Approximation and Newton's Method

3. The Attempt at a Solution
This is a question where I do not know where to start. I know I am supposed to find the height of the box using the volume formula and am given the volume, but I don't know how to calculate the length. To me this seems to be a change in value question, where the volume is changing, but I don't think this is right :tongue:. Could anyone be of assistance here please to get me on the right track for this question? Thanks in advance.

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#### foxjwill

first of all, Tangent Line Approximation and Newton's Method will be of no help to you here.

Code:
. . . . _______________ . . . .
.      |               |      .
.      | s           s |      .
.______|               |______.
|   s                     s   |
|                             |
|                             |
|                             |
|                             |
|                             |
|                             |
|   s                     s   |
|______                 ______|
.      |               |      .
.      | s           s |      .
. . . .|_______________|. . . .

|<---------- 10cm ----------->|
As to solving the problem, try looking at my picture.

EDIT: you shouldn't need any calculus to do this.

#### Emethyst

Thanks foxjwill, I just put down both the tangent line approximation and Newton's Method because this is a question from those sections in my Calculus unit :tongue:. So from what I can see, 10-2s=L (or A=L^2-4s^2, V=L^2s) , where s is what I am looking for. I need to find L first then plug it into one of the formulas to find s. Would this be a case of substituting one equation into another, or would this be wrong?

*L is the variable I assigned to the base sides, in case no one knew where that came from.

#### foxjwill

Thanks foxjwill, I just put down both the tangent line approximation and Newton's Method because this is a question from those sections in my Calculus unit :tongue:. So from what I can see, 10-2s=L (or A=L^2-4s^2, V=L^2s) , where s is what I am looking for. I need to find L first then plug it into one of the formulas to find s. Would this be a case of substituting one equation into another, or would this be wrong?
Yup. it would be a case of substituting one equation into another.

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