# An open -top box is to be made by cutting small congruent squares from the corners of a 12-by12-in. sheet of tin and bending up the sides. How large should the squares cut from the corners be to make the box hold as much as possible?

##### 1 Answer

Apr 27, 2015

If the squares cut from the corners are

The open-top box will have

a height of

a width of

and a length of

So it's volume will be

Critical points occur when the derivative (

Therefore the maximum volume is achieved by by cutting out squares that are