 Okay, I've got a scale model of a house a scale model of house where one centimeter is equal to one meter now I know that a centimeter is a hundredth of a meter take life in my own hands and try and draw a house Now I'm gonna have a length here and a width and a height And when I make the real house, I'm gonna have to make everything bigger So that L is gonna have to be a hundred times bigger that W is gonna have to be a hundred times bigger And that H is gonna have to be a hundred times bigger. Now the question is what do I need to calculate to figure out how much paint I'll need and how much wood I'll need And they're actually different So when we scale this up all those surfaces are gonna be covered with paint and I'm gonna need more paint and all those Construction materials are gonna be scaled up and much bigger and so I'm gonna need more wood Now the wood goes as the volume the mass of the wood is its density Which is not gonna change times its volume and the volume is gonna go as the length times the width Times the height if this were exactly some kind of rectangular solid It would be exactly the length times the width times the height But because we have roofs and possible extra shapes around the back. It's only going to scale that way So if I double the length, I should double the volume if I double the width I should double the volume if I double the height I should double the volume and if I multiply each of them by a hundred Then I'm gonna get a hundred cubed times as much Which is a million times as much which we basically knew as soon as we realized we're after the volume Because remember the volume scale is the cube of the length and so if we increase our length by a factor of a hundred Then we increase our volume by a factor of a hundred cubed Now what about paint? Well paint just covers the surface of things and the surface of things is an area And so this area here is a height times a width this area here Is a length times a height and so on and we know that area scales as the square of the length And so we know that the area will go as length squared And so if we increase our length by a factor of a hundred then we'll increase our area by a factor of a hundred squared Which is ten thousand