A frustum of a solid right circular cone has circular faces of radii 2 cm and 4 cm and a height of 5 cm. A cylindrical hole of radius 1 cm was bored down the axis of symmetry of the frustum from one circular face to the other. Find the distance between the center of mass of the solid formed and the center of its larger face.
A uniform solid hemisphere of radius 4 cm and a uniform solid right circular cylinder of height 9 cm and radius 4 cm are joined by their bases to form a composite solid. The centers of the bases coincide at the point . Given that the hemisphere and the cylinder have the same density, determine the distance between and the center of mass of the composite solid.
A uniform solid right circular cone of height 7 cm and base radius 3 cm and a uniform solid hemisphere of radius 3 cm are joined by their bases. The centers of their bases coincide at a point . Given that the hemisphere’s density is twice that of the cone, find the distance from to the center of mass of the composite body.