Minimum Surface Area Investigation Introduction For my maths coursework I have been asked by a tin manufacturing company to minimise the amount of metal required to produce cans. The cans must be cylindrical and come in four different sizes: 1. 300 cm3 2. 400 cm3 3. 600 cm3 4. 750 cm3 I have been asked to come up with a reverse formula to enable them to find the height and radius for any given formula of a cylindrical tin that will ensure that the surface area is a minimum. Method I...
minimum surface Area for a volume of 900cm3 my results were:

• Cylinder – 516.0315049 cm3

• Sphere - 450.7950419 cm3

• Cube - 559.3018511 cm3

So from these results I can see that as I previously stated the sphere is the best 3-D shape to store any volume water because it has the smallest surface area. However the manufacturing company has chosen the cylinder because although a sphere has a smaller surface area it would be very difficult to stack on supermarket shelves and store safely, whereas a cylinder can be kept upright.