# Optimal boxes

- Author:
- Simona Riva

- Topic:
- Calculus, Optimization Problems

*Cut out four congruent squares from a cardboard sheet, so that the remaining part can be folded to create the box (with no top) having max volume.*Use the sliders in the construction to set the lengths of

*base*and

*height*of the sheet. Move the

*green point*on the sheet base to modify the cutout area. If

*x*is the length of the

*side*of the cutout

*square*, what's the length of

*x*that will create a box with maximum volume? (You can also move the

*blue point*at the sheet top right vertex to change its perspective view.)