How Do You Formulate a Polynomial for Volume in This Prism Problem?

AI Thread Summary
The discussion focuses on formulating a polynomial for the volume of a square prism, given that the sum of the prism's length and the perimeter of its base equals 100 cm. The initial attempt at deriving the volume function includes incorrect elements, particularly incorporating the perimeter into the volume calculation. Participants suggest solving for the length in terms of width and height to correctly express the volume as length times width times height. Ultimately, the problem is clarified as a rectangular box, leading to a successful resolution of the question. The importance of correctly defining the dimensions and relationships in the problem is emphasized.
MrJamesta
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Homework Statement


A package sent by a courier has the shape of a square prism. The sum of the length of the prism and the perimeter of its base is 100cm. Write a polynomial function to represent the volume V of the package in terms of x.
width and height are in x centimeters, length is in y centimeters

The Attempt at a Solution



4x+y=100
4x+y-100
V(x)=(x^2)(y)(4x+y-100)
V(x)=(4x^3y + x^2y^2 - 100x^2y)
V(x)=x^2y(4x+y-100)

This is as far as I got, am I going in the right direction? Where did I go wrong?
 
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MrJamesta said:

Homework Statement


A package sent by a courier has the shape of a square prism. The sum of the length of the prism and the perimeter of its base is 100cm. Write a polynomial function to represent the volume V of the package in terms of x.
width and height are in x centimeters, length is in y centimeters

The Attempt at a Solution



4x+y=100
4x+y-100
V(x)=(x^2)(y)(4x+y-100)
V(x)=(4x^3y + x^2y^2 - 100x^2y)
V(x)=x^2y(4x+y-100)

This is as far as I got, am I going in the right direction? Where did I go wrong?
From your first equation above, solve for y to get the length of the prism in terms of x.

Your formula for volume is incorrect, I believe, but I don't know how the problem is defining the term "prism." Is it just a rectangular box? If so, the volume is length x width x height. The volume shouldn't also include the perimeter.
 
Mark44 said:
From your first equation above, solve for y to get the length of the prism in terms of x.

Your formula for volume is incorrect, I believe, but I don't know how the problem is defining the term "prism." Is it just a rectangular box? If so, the volume is length x width x height. The volume shouldn't also include the perimeter.

Thank you very much, I was able to solve the question. And yes, it was just a rectangular box.
 

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