Use MATLAB to solve each problem.

Some of the commands you may need on this assignment are: syms, int, solve, and double

3. A hemispherical tank (half-sphere) with a radius of 3 m is full of water. (The density of water is = 1000 kg/m3 and the acceleration due to gravity is a = 9.8 m/s2.

(a) How much work is needed to pump all the water out of the top of the tank.

(b) How much work is needed to pump out the top so that the remaining water has a height of h

m. (Your answer will be in terms of h.)

(c) What is the height of the water left in the tank after 100, 000 J of work has been done?