Q9 Box problem (MEDIUM)
A company produces juice containers which have the shape of a box with squares on the base and the top, and a capacity of 2 litres.
- Find a formula for the surface area, , of the container in terms of the apothem of the container. The apothem is the segment from the centre of the square to the midpoint of one of its sides.
- Find the apothem of the container which will minimize the cost of the material required to make the box.
- Find the corresponding height and side of the square.
Answers and workings.