1. ## deriving

I was just wondering this. When you differentiate the volume of a sphere you find the surface area of a sphere. When you differentiate the area of a circle, you get the circumphrence of a circle. I have tried but I can't seem to apply this concept to cubes and squares. Like say for example the volume of a cube is x^3. When you differentiate that you get 3x^2, which isn't the surface area of the cube (at least I think so). also, if the area of a box was x^2, when you differentiate that you get 2x, is is not the perimeter of that box. Maybe I'm not applying the right idea here, but I was just wondering. What do you guys think

2. Originally Posted by nertil1
I was just wondering this. When you differentiate the volume of a sphere you find the surface area of a sphere. When you differentiate the area of a circle, you get the circumphrence of a circle. I have tried but I can't seem to apply this concept to cubes and squares. Like say for example the volume of a cube is x^3. When you differentiate that you get 3x^2, which isn't the surface area of the cube (at least I think so). also, if the area of a box was x^2, when you differentiate that you get 2x, is is not the perimeter of that box. Maybe I'm not applying the right idea here, but I was just wondering. What do you guys think
Error in logic.
Just because it works for circles and spheres does not mean that it works for cubes and squares.

Though, that is an interesting thing, I once realized that myself but my analogy was better. I assumed that if we can define a 4 dimensional ball then its Total space (however it is called) when differenciated will result in the volume of a 3-d sphere.

3. Originally Posted by nertil1
I was just wondering this. When you differentiate the volume of a sphere you find the surface area of a sphere. When you differentiate the area of a circle, you get the circumphrence of a circle. I have tried but I can't seem to apply this concept to cubes and squares. Like say for example the volume of a cube is x^3. When you differentiate that you get 3x^2, which isn't the surface area of the cube (at least I think so). also, if the area of a box was x^2, when you differentiate that you get 2x, is is not the perimeter of that box. Maybe I'm not applying the right idea here, but I was just wondering. What do you guys think
It does work you are just using the wrong parameter to represent the
size of the square or cube. If you work in terms of the half-side rather
than the side you will find this works for the cube and the square.

The idea is that you are modelling the higher dimensional measure of the
body as though it were the sum (integral) of shells.

RonL