Let h, s, v be the height, surface area and volume, respectively, of the small drum, and let H, S, V be the height, surface area and volume of the large drum. Since the drums are similar, and . Since you know H/h, s and v, you can find S and V.
Oil is stored in either small drums or large drums. The shapes of the drums are mathematically similar.
A small drum has a volume of 0.006m3 and a surface area of 0.2m2
The height of a large drum is 3 times the height of a small drum.
1) Calculate the volume of a large drum?
How do I go about doing this as I know it's not 3 x 0.006
2) The cost of making a drum is £1.20 for each m2 of surface area. A company wants to store 3240m3 of oil in large drums. Calculate the cost of making enough large drums to store this oil?
Any help would be much appreciated.
That's a property of similar figures. You can prove it in some specific cases. For example, suppose drum are cylinders, the diameter of the small drum is r and that of the large drum is R. By the definition of similarity, R / r = H / h. Let's call this ratio k. Then (top and bottom circles plus the side). So, . The principle is true for arbitrary similar figures, though. One probably needs calculus to prove it in general.