# Mathematical Modelling of a Can.

Essay by eviiil October 2005

Mathematical Modelling: Can of Drink

1.)

Consider a drink can of capacity 330ml. Draw a diagram, or a number of diagrams which show all the features of the can.

Height: 11.5 cm

Diameter (top): 5.42 cm

Diameter (middle): 6.5 cm

Diameter (bottom): 5 cm

Capacity: 330ml

Vcan: 330 cm"

2.)

Use your diagrams of part 1 to help you choose a simple three dimensional shape which models this can and define suitable variables for this shape.

- I have used a cylinder to model a regular can of drink since it has similar features as a can, one of them being that one can unfold the cylinder into a rectangle (the sides) and two circles (top and bottom) which one can do with a can as well.

Solid Cylinder:

Area: A = 2ÃÂrh + 2ÃÂr"

Volume: V = (Area of base) x height

V(r) = ÃÂr"h

1ml = 1cm"

Variables are r and h

h = height

3.)

By considering the volume of this shape, establish a relationship between the variables defined in part 2.

h = 11.5 cm ; r = 3.25 cm ; d = 6.5 cm

V(r) = ÃÂr"h h =

- I am using the relationship of the Volume Formula with the variables r and h to eliminate h as an unknown variable. By doing this step I can substitute h with the rearranged Formula, meaning that only r is left as an unknown variable.

4.)

Find a function, S, in terms of one of the variables defined in part 2, where S is the total Surface Area of the can.

330cm" = V = 2ÃÂr"h

A = 2ÃÂrh + 2ÃÂr" = 2ÃÂr(r + h)

- I substituted h with the equation I derived from the Volume formula.