A regular tetrahedron of height h has a tetrahedron of height xh cut off by a plane parallel to the base. When the remaining frustrum is placed on one of its slant faces on a horizontal plane, it is just on the point of falling over. (In other words, when the remaining frustrum is placed on one of its slant faces on a horizontal plane, the projection of the center of gravity G of the frustrum is a point of the minor base of this slant face.)
Show that x is a root of the equation x3+x2+x=2. geometry3D geometrytetrahedronfrustumspheretrigonometryintegration