Planetary Cooling The Surface Area to Volume Ratio The total heat contained in a planet depends upon its volume. However, as the planet cools, this heat escapes through the planet's surface. The rate at which a planet cools will in part be determined by the ratio of its surface area to its volume. For a spherical planet of radius r , the volume is 4 r3/3 and the surface area is 4 r2. The ratio of these two quantities may be written as: Incidentally, the same basic idea explains why crushed ice cools a drink faster than ice cubes: the small bits of crushed ice have a greater total surface area than the same Questions: Why does crushed ice cool something faster than large cubes of ice? Why does crushed ice melts faster than a large cube of ice with the same mass? Crushed ice in your drink cools it faster than ice cubes. Let's look at the reason why. The same ice cube, broken up into 27 smaller pieces. the amount of ice is exactly the same. Each little piece is 1 cm in length. Heat can only enter a cube through its six sides. Surface area Volume Surface