Math Calculus Word Problem
posted by Ashley V .
an 18 inch by 20 inch sheet of cardboard is cut and folded to make a box for the great pecan company.
a. write a polynomial funtion to model the volume of the box.
how can i graph this?
c. the company wants the box to have a volume of 224 cubic inches. write an equation to model this situation.
d. find a positibe integer for x.

Math Calculus Word Problem 
Reiny
I will asssume that you are going to cut equal squares from each of the four corners to do this.
Let each side of a square be x inches.
then the length of the box will be 202x
its width will be 182x in
and its height will be x in
since Vol = length x width x height
Vol = x(202x)(182x)
make a table of values, noting there are zeros at x=0, x=10 and x=9
b) x(202x)(182x) = 224
c) expanding this and simplifying I got
x^3  19x^2 + 90x  56=0
I ran this through the following cubic equation solver
http://www.1728.com/cubic.htm
and got x=6.529, the other two answers are extraneous.
(check my work, I tend to get careless at this time of night)
Respond to this Question
Similar Questions

Calculus
You are given a 60 inch by 30 inch piece of cardboad and asked to make a sixsided box. If the cardboard is cut along the lines shown, what will the dimensions of the box with maximum volume? 
Math
From an 8 inch by 10 inch rectangular sheet of paper, squares of equal size will be cut from each corner. The flaps will then be folded up to form an opentopped box. Find the maximum possible volume of the box. 
Math
From a 10inchby19inch piece of cardboard, 3inchsquare corners are cut out, as shown in the figure above, and the resulting flaps are folded up to form an open box. Find the surface area and volume of the open box 
MATH help
A box with no top is to be constructed from a piece of cardboard whose Width measures x inch and whose length measures 3 inch more than the width the box is to be formed by cutting squares that measure 1 inch on each side of the 4 … 
Calculus
An open top box is made by cutting congruent squares from the corners of a 12 inch by 9 inch sheet of cardboard and then folding the sides up to create the box. What are the dimensions of the box which contains the largest volume? 
Algebra
A box with a lid is to be cut out of a 12 inch by 24 inch sheet of thin cardboard by cutting out six xinch squares and folding them. What are the dimensions to two decimal places of all possible boxes that will have a volume of 100 … 
Maths Calculus
a sheet of cardboard is to be folded up to make a closed box. If the cardboard measures 55 cm by 80cm calculate the maximum volume of the box that can be made from this sheet of cardboard 
Algebra 1 (Reiny!)
A piece of 8.5by11inch cardboard has identical squares cut from its corners. It is then folded into a box with no lid. The volume of the box in cubic inches is 4c^3  39c^2 + 93.5c, where c is the side length of the missing squares … 
math
Identical square are cut from each corner of an 8 inch by 11.75inch rectangular piececof cardboard.the sides are folded up to make a box with no top . if the volume of the resulting box is 63.75 cubic inches how long is the edge of … 
Calculus
Equal squares of side length x are removed from each corner of a 20 inch by 30 inch piece of cardboard, and the sides are turned up to form a box with no top. Write the volume V of the box as a function of x.