Final answer:
Calculate the work done by integrating the small portions of work done to move water, account for different heights in the tank.
Step-by-step explanation:
The subject of this question is physics, specifically the concept of work and energy. To calculate the work done in pumping water out of the tank, we can use the equation for work which is Work = Force x Distance. Calculate the force used to move each small portion of water, then multiply by the distance it needs to go. The total work is the integration of these small works.
However, since water is pumped out from different heights, we need to use calculus for a precise calculation. The force required to move a small portion, dh, is F = dV x g x rho, where 'rho' is the density of water. We know that the volume of a small portion of the hemisphere, dV, is pi x h^2 x dh. So, the force becomes F = pi x h^2 x dh x rho x g. The distance this portion of water needs to travel is L + R - h. Hence, the work done to move this small portion, with respect to h, is dW = F x distance = pi x h^2 x (L + R - h) x rho x g dh. Integrate this from h = 0 to h = R to calculate the total work, and remember to convert this to Megajoules (MJ), knowing that 1 MJ = 10^6 Joules.
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