# Rectangular Package

• Oct 4th 2010, 03:34 PM
lightbanders
Rectangular Package
A Rectangular package sent by a delivery can have a maximum combined length and girth (perimeter of a cross section) of 120 inches.

Here, there is a picture, which is a 3D package, with length of y, and with of x.

The problem is the following: Give a formula for the volume of the package.

Thank you very much
• Oct 5th 2010, 04:50 AM
earboth
Quote:

Originally Posted by lightbanders
A Rectangular package sent by a delivery can have a maximum combined length and girth (perimeter of a cross section) of 120 inches.

Here, there is a picture, <== I can't see an image of the package (Thinking)
which is a 3D package, with length of y, and with of x.

The problem is the following: Give a formula for the volume of the package.

Thank you very much

1. I've made a sketch of the package (see attachment)

2. Since there are only given 2 measures I assume that the package should have a square cross-section.

3. The volume of the package is calculated by:

$V = l \cdot x$

with the constraints

$l + 4x = 120~\implies~l=120-4x$

4. Therefore the volume is a function of the width of the package:

$V(x)=(120-4x) \cdot x = 120x-4x^2~,~0\leq x\leq 30$
• Oct 5th 2010, 04:56 AM
Wilmer
Quote:

Originally Posted by lightbanders
Here, there is a picture, ...

We can't see any picture.

With what you gave us, all I can tell you is that volume calculation
of a rectangular package also requires height.
• Oct 5th 2010, 05:47 AM
Quote:

Originally Posted by lightbanders
A Rectangular package sent by a delivery can have a maximum combined length and girth (perimeter of a cross section) of 120 inches.

Here, there is a picture, which is a 3D package, with length of y, and with of x.

The problem is the following: Give a formula for the volume of the package.

Thank you very much

Girth = $2(h+x)$

$y+2(h+x)=120$ inches

$\Rightarrow\ h=\frac{120-y}{2}-x$

$V=yhx=yx\left(\frac{120-y}{2}-x\right)$ cubic inches