Cube rule

The cube rule is a way of understanding how the volume of an object changes when its size changes. So imagine you have a tiny cube that is 1 inch long on each side. If you take that cube and make it 2 inches long on each side, you might think that the volume of the cube simply doubles. However, according to the cube rule, the volume actually increases by 2^3, which is 8 times the original volume!

Okay, let's break that down a bit. When we say "to the third power," that means we want to multiply a number by itself three times. So, if the original cube's volume was 1 cubic inch, multiplying that by itself three times gives us:

1 x 1 x 1 = 1 cubic inch

Now, if we double the size of the cube, making it 2 inches long on each side, the calculation would look like this:

2 x 2 x 2 = 8 cubic inches

So even though we only doubled the length of each side, we actually ended up with 8 times the volume! This is because when you multiply a number by itself three times, you end up with a much bigger number than if you just double or triple it.

The cube rule isn't just for cubes, though. It applies to any object where we are changing all three dimensions. For example, if you have a rectangular prism that is 3 inches long, 2 inches wide, and 1 inch tall, its volume is 3 x 2 x 1 = 6 cubic inches. If you make that same prism 6 inches long, 4 inches wide, and 2 inches tall, its volume becomes 6 x 4 x 2 = 48 cubic inches - a 8-fold increase, just like with the cube.

So, in summary, the cube rule tells us that when we increase the size of an object by doubling its length, width, and height, its volume increases by 8 times.