College textbooks

College textbooks may be in the top-ten of the worst things for sale, ever. It’s not bad enough that the universe makes you feel worthless if you don’t get a degree, and then laughs at you when you want a job. No, along the four- or five-year journey to your worthless diploma, they make you buy dozens of textbooks.

The future has brought slight reprieve to the textbook problem – you can buy them online for cheap, get free shipping, and resell them for more than the snotty guy at the campus bookstore wants to give you when the class is over. But the fundamental issue remains that introductory calculus, or chemistry, or whatever, has not changed in at least twenty years. The only difference is the word problems have changed.

Skrillex buys an ice cream cone whose height is h and radius r, topped with a sphere of ice cream with radius 1.1r. His friend Deadmau5 texts him on an iPhone 4, and while he texts back, the ice cream melts and runs into the cone. The cone has a leak which allows the melted ice cream to run out the bottom at rate 0.031r³ per minute (t). Express the surface area of the cone filled with melted ice cream as a function of time. Do not use rage faces in your solution.