Melting is due to the heat entering the ice, and therefore, it changes into water. The heat comes from the environment. So the more exposed to the environment (more surface area), the quicker it melts. But you can't just use the surface area. You also have to consider the mass. How much do you have to melt? Let's say you have 2 cups of water forzen into ice, and it has a surface area of 4. And you have 2 cups of water frozen into ice, and it has a surface area of 5. Then the one with the surface area of five will melt faster. Everything is dependent on the mass to surface area ratio. The first block of ice has a mass to surface area ratio of 2 (4:2 > 2) The second one has a one of 5/2, or 2.2 The one with the higher surface area to mass ratio will melt faster, because it has more surface area per cup of water.
