A square piece of tin of side 18 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that the volume of the box is maximum? Also, find the maximum volume.

Explanation

`A-H,G-F,E-D,B-C`
volume of box`=y^2x`
`=y^2(9-y/2)`
`=9y^2-y^3/2`
`V(y)=V\'(y)=0`
`V\'\'(y)<0`
`18y-(3y^2)/2=0`
`3(y)(6-y/2)=0`
`y=0 or y=12`
`V\'\'(y)=18-6y/2`
`=18-36`
`=-18<0`
`9-y/2=9-12/2`
`=3`