SOLUTION: Please help! I have been struggling with this question all morning! An open topped box is to be made by cutting out identical squares from the corners of a rectangular piece of

Algebra ->  Rational-functions -> SOLUTION: Please help! I have been struggling with this question all morning! An open topped box is to be made by cutting out identical squares from the corners of a rectangular piece of      Log On


   

Question 964890: Please help! I have been struggling with this question all morning!
An open topped box is to be made by cutting out identical squares from the corners of a rectangular piece of cardboard then folding up the resulting flaps. Thus, if the side of each removed square has length 'x' then the box height will also be 'x'. If the cardboard has dimensions 70cm by 50cm find an expression for the volume of the box V(x) in terms of 'x'. What is the domain of this function? What sort of function is it (quadratic, cubic, rational or...)?

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Assign Variables, for EVERYTHING.
w, width of rectangular cardboard
L, length rectangular cardboard
x, the edge length of the removed square picees, same as box height

Try to draw a picture of the description and label everything.

Area of the resulting base of the formed box after folding the flaps,
%28w-2x%29%28L-2x%29

The volume, V(x) will be the area multiplied by the height dimension:
highlight%28V%28x%29=x%28w-2x%29%28L-2x%29%29

That is a cubic function. You can fully multiply completely if you want in general form.

V%28x%29=x%28wL-2Lx-2wx%2B4x%5E2%29
V%28x%29=4x%5E3-2Lx%5E2-2wx%5E2%2BwLx
highlight%28V%28x%29=4x%5E3-%282L%2B2w%29x%5E2%2BwLx%29

To finish the specific equation for your description, substitute the described values:
w=70
L=50
and compute any constants and coefficients.