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Calculating the cut out section of a box

  • Thread starter Emethyst
  • Start date
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.
 
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.
 
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.
 
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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