To calculate the centroid of a cone, it seems that you have to use calculus. It comes out to be h/4, where h is the height from the base of the cone. But intuitively I thought that the centroid would have been h/3 because that's a triangle's centroid, and the cone can be obtained by rotating a triangle. Now notice that if you slice the cone in half so that you have two halves with semi-circle bases, the height of the centroid of each half should still be h/4. Now if you slice in half again so that you have quarter cones, the height of the centroid of each of the quarter cones will be h/4 again. You can continue slicing this way until you have virtually an infinite number of fraction cones, each with their bases being a tiny slice of a circle. Each of these should have their centroid height be h/4 You can also obtain one of these cone slices by taking a right triangle and rotating it by a tiny angle theta. But the triangle's centroid itself is h/3. So the moment you rotate it a little bit the centroid of the solid generated jumps down to h/4. I'm not too sure what I'm asking here, but I just find this "jump" to be strange and am looking for some intuition as to why this happens. Can anyone explain?