Acardboard box without a top is to have volume 62500 cubic cm. find the dimensions which minimize the amount of material used.

A cardboard box without a lid is to have a volume of 32,000 cubic cm. Find the dimensions that minimize the amount of cardboard used

. ans: base 40 x 40, height = 20  

Solution:  

The typical box might look like the one below  

where . In addition we have xyz = 32000 ,so we need to minimize .  

We have,  

From the geometry of the problem  so y = x. So  or x = 40.  

Finally, y = x = 40 and z = 32000/(xy)=20.

is this part of a question or something