Since heat touching the surface of an ice cube causes it to melt, is it

better for an ice cube to have a large surface area or a small surface

area? I'm thinking that the bigger the surface area the slower it will melt am I right

Well, it depends on the size of the ice cub and how much heat is being added. if its smaller and it has large amounts of heat being added it will melt fast, if its small and low amounts of heat are being added it will melt slower, if its a big cubs and large amounts of heat are being added it will melt slower than the small cub at the same temp but if its getting more heat than the small cub its should melt faster, ect. but in your case id say your right and bigger surface slower melt.