One piece is cylindrical with a hemispherical hat (the flat face of hemisphere rests flush on top of the flat face of the cylinder). The diameter of the cylinder and hemisphere are identical at 2r inches, and the height of the cylinder is 2r inches. The second piece is a cube with a mountedcylinderon it such that one of the flat facesof the cylinder is resting on the top face of the cube. The four edges of the cube are tangential to the circle of the cylinder resting on it. The side of a cube has a length of 2r inches and the height of the cylinder is r inches. The third piece is a cube with a mounted hemisphere on it such that the flat face of the hemisphere is resting on the top face of the cube. The four edges of the cube are tangential to thecircle of the hemisphere resting on it. The side of a cube has a length of 2r inches and the radius of the sphere is r inches. Required:
Which piece will solidify the fastest and which piece the slowest?