Dimensions

Question

An open box is to be made out of a 8-inch by 18-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.

Answer 1

Let x = length of a side of one of the square cutout corners

 

After cutting the cardboard and folding, we get a box (with no top).  The bottom of the box is a rectangle with dimensions 8-2x by 18-2x.  The height of the box is x.  

 

V(x) = volume of box 

 

       = x(8-2x)(18-2x) = x(4x² - 52x + 144)

 

V(x) = 4x³ - 52x² + 144x

 

Set V'(x) = 0 to find the value of x which gives maximum volume.  

Answer 2

Hi Sydney,

 

Is this question from a calculus course?

 

That's the only way to calculate the largest volume.

 

Dan