Volume

**dc52789** · January 26th 2009, 08:40 PM

An open box is made from a rectangular piece of material 12" by 16" by cutting equal squares from each corner and turning up the sides. Let x be the length of each side of the square cut out of each corner. Write the volume V of the box as a function of x.

**earboth** · January 26th 2009, 08:55 PM

Originally Posted by dc52789

An open box is made from a rectangular piece of material 12" by 16" by cutting equal squares from each corner and turning up the sides. Let x be the length of each side of the square cut out of each corner. Write the volume V of the box as a function of x.

The volume of such a box is a prism.

$V_{prism} = (base\ area) \cdot height$

The base area is a rectangle with

$a_r = (16 - 2x) \cdot (12 - 2x)\ ,\ x\in [0,6]$

The height of the prism is x. Thus the equation of the function is:

$V(x)= x \cdot (16 - 2x) \cdot (12 - 2x) \ ,\ x\in [0, 6]$

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