The inspiration of this mathematical investigation comes from an essential aid that helps me and my friend to get through the IB ice cream Whenever my friends and I are stressed about the workload from the IB we would work together with some ice cream by our side to cheer us up However it would always frustrate us when we concentrate on work for a long while only to find that the ice cream has melted Therefore when I had to come up with a topic for the Maths IA I thought it would interesting to connect calculus maths differentiation and integration an abstract concept to something that I not only love but also something that is real something that I can touch and see or even to eat Eventually I chose to do it on ice cream which is something I cannot live without I have always been a curious learner So when I came up with the idea I was very excited by it and started to think how ice cream melts In my observation I found out that ice cream melts faster when it is more exposed in the air In other words the rate at which the ice cream melts is actually proportional to its surface area I find that quite interesting and decided to look more into the 3D shapes of ice cream The aim of this investigation is to compare the melting rates of different solids of the ice cream It will be looking at basic solids of ice cream such as sphere hemisphere cubes and cuboids as stored in containers as well as some more interesting shapes i e platonic solids tetrahedron and dodecahedron The rate can be calculated by using calculus differentiation and integration I hope that through this exploration I can find the solid with the slowest and fastest melting rate and from that see if the abstract mathematics coincides with real life practicality