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

[MrJamesta]

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?

 

[Mark44]

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.

 

[MrJamesta]

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.