Square–cube law

The square-cube law is a big idea that explains how things can change as they get bigger or smaller. Imagine you have a cube-shaped toy that is 1 inch on each side. If you multiply 1 inch by itself twice (or times itself twice), you get the surface area of this toy. This would be 1x1x6 or six square inches total.

Now, if you multiply 1 inch by itself three times (or times itself three times), you get the volume of the cube-shaped toy. This would be 1x1x1 or one cubic inch total.

So what does all of this mean? Well, the square-cube law says that as you make the toy bigger or smaller, its surface area and volume change in different ways.

For example, let's say you make the toy twice as big. Instead of being 1 inch on each side, it's now 2 inches on each side. If you use the same math we did before, you'll find that the surface area is now 2x2x6 or 24 square inches - this is 4 times the original surface area. However, the volume is now 2x2x2 or 8 cubic inches - this is 8 times the original volume.

What if you make the toy even bigger? Let's say you make it 10 inches on each side. If you use the same math we did before, you'll find that the surface area is now 10x10x6 or 600 square inches - this is 100 times the original surface area! However, the volume is now 10x10x10 or 1000 cubic inches - this is 1000 times the original volume!

So as you can see, the square-cube law shows that things change in different ways as they get bigger or smaller. This is a really important idea that helps scientists and engineers understand how the world around us works.