(Solved): 2. A spherical tank full of oil has a radius of \( 20 \mathrm{~m} \) and has a \( 2 \mathrm{~m} \) ...

2. A spherical tank full of oil has a radius of \( 20 \mathrm{~m} \) and has a \( 2 \mathrm{~m} \) spout at the top. Note that the density of the oil is \( \rho=900 \mathrm{~kg} / \mathrm{m}^{3} \) and the acceleration due to gravity is \( \mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2} \). (Approximate answers acceptable for all parts) (a) How much work is needed to pump all of the oil out of the top of the tank? (b) How much work is needed to pump out the top so the remaining oil has a depth of \( \mathrm{h} \) meters? (c) What is the depth of the oil in the tank after \( 100,000,000 \pi \mathrm{J} \) of work has been done?