Yes, that's exactly what happens. Think of a point in an n-dimensional hypercube and the pyramids made by connecting it to the n many opposite faces. These pyra

Yes, that's exactly what happens. Think of a point in an n-dimensional hypercube and the pyramids made by connecting it to the n many opposite faces. These pyramids each have volume 1/n times the hypercube's volume. And in the same way, in n dimensions, any tapering figure has volume given by its height times its base divided by n.