# Complimentary samples

- Author:
- Simona Riva

- Topic:
- Cylinder, Derivative, Solids or 3D Shapes

Advertising is the very soul of trade, but it has costs!
Your advice is needed again to choose a nice (and cheap!) packaging for some complimentary boxes, containing a smaller version of the pasta that you have created.

## Option no. 1 - Cylindrical boxes

These complimentary boxes will be shaped as small cylinders, having a volume of cm

^{3}. The top and the bottom will be transparent, made with a plastic material that costs €2/m^{2}, and the side is made with fine cardboard, that costs €10/m^{2}.Find the radius *r* of the base and the height *h* of the box that minimize its cost.

## Option no. 2 - Rectangular parallelepiped

These classic complimentary boxes will be shaped as rectangular parallelepipeds, having the same volume of the cylindrical ones, and height 4

*cm*. They will be built using the same materials for the top and the side as the cylindrical ones.Find the length *l* and width *w* of the base of the box that minimize its cost.
What do you observe?

## Compare costs, and decide

How much does a cylindrical box cost? And the "classic" one? (Round costs to 2 decimal places) So the cheapest complimentary box is...