A reservoir in the form of a straight prism with triangular base is shown in the figure.
Its vertical faces are isosceles triangles of height 3 m and base 2 m, its length is 6 m, it is near the surface of the Earth, and it is full of water, which will be pumped to a height of 1 m above the reservoir.
Denote by x the height in meters measured from the bottom of the reservoir.
a. What is, at first approximation, the volume of the layer of water between the heights x and x + Δx?
b. What is, at first approximation, the work required to pump that layer of water to a height of 1 m above the reservoir? Recall that the density of water is 1000 kg/m3, and gravitational acceleration at the surface of the earth is g ≅ 9.8 m/s2.
c. What is, in Joules, the work required to pump all the water from the reservoir to a height of 1 m above the reservoir?