Here is the first problem from my PSET

1. An enormous mountain of height 7500 meters is shaped like a cone With a base radius of 5000 m. Due to various geological factors such as pressure and heat, the density of the mountain varies With the height h and is given by the function p(h) kg/m3. (a) Write a general Riemann sum that approximates the mass of the mountain. (b) Write an integral giving the exact mass of the mountain. 1 m, then the mass of the mountain Use the following fact to Check your answer if you like: If p(h) = is approximately 4.957 X 107 kg