Process
Ice melts due to the application of heat, which increases the movement of molecules. For ice, whether it is an ice cube or an iceberg, melting starts on the outside. As heat reaches more molecules, the process speeds up. The shape of the ice affects the rate of melting due to surface area.
Surface Area
Different shapes have different surface areas. The larger the surface area, the faster ice melts. Find the mathematical formula and calculate the surface area for any given shape, like a cube, square, triangle or cylinder. Compare the surface area of one shape with the surface area of another shape. The shape with the larger surface area exposed to heat has the faster rate of melting.
Exposure
Exposure refers to the amount of surface area that comes into contact with heat. For example, the more of an iceberg that sticks out of the ocean, the faster it melts. Cover an ice cube and only allow one side to be exposed to light and you slow down the melting process. The shape of ice controls the melting rate as some shapes expose more surface area by the way they are designed, especially when the ice is sitting on an object like a floor or table.
Thickness
Because ice melts first at the surface and then downward, the thickness of the shape does not affect the melting rate. A thick piece of ice with large amounts of surface area will melt faster than a thin block of ice with very little surface area. It all depends upon the heat speeding up the molecules in the ice, and the more surface the more the molecules move.