# Thread: Word problem involving rectangle area...

1. ## Word problem involving rectangle area...

A rectangular sheet of metal measures 50cm by 40cm. Equal squares of side x cm are cut from each corner and discarded. The sheet is then folded up to make a tray of depth x cm. What is the domain of possible values of x? Find the value of x which maximizes the capacity of the tray.

I can handle the differentiation part. Just need the equation

2. Originally Posted by struck
A rectangular sheet of metal measures 50cm by 40cm. Equal squares of side x cm are cut from each corner and discarded. The sheet is then folded up to make a tray of depth x cm. What is the domain of possible values of x? Find the value of x which maximizes the capacity of the tray.

I can handle the differentiation part. Just need the equation
1. You can't cut off more than $20\ cm\times20\ cm-squares$ because then the width of the sheet would be zero. Therefore

$D=\{x|0\leq x \leq 20\}$

2. the volume of a prism is calculated by:

$V = (base\ area) \cdot height$

The base area is a rectangle which measures (50-2x)(40-2x)

3. Therefore the function of the volume wrt x:

$V(x)=(50-2x)(40-2x)\cdot x$