A tank has the shape of a right prism whose parallel extremities are isosceles triangles, as in the figure above. It is 5m high, 4m wide and 6m long, and it is filled with water. We want to calculate the work required to pump all of its water through the pipe 1 m above the tank.

(i) Let x be the height in meters measured from the bottom of the reservoir. The weight of a thin layer of water between heights x and x+?x is approximately P(x)?x . What is P(x)? P(x)=

Express the answer with a formula. We recall that the density of water is ?=1000Kg/m3 and that the gravitational acceleration at the surface of the earth is g=9.8m/s2.

(ii) The work in Joules required to pump this thin layer of water 1 m above the reservoir is approximately w(x)?x . What is w(x)? w(x)=

Express the answer with a formula.

(iii) Using the previous results, determine the work required to pump all the water 1 m above the reservoir. Give its numerical value to within 3 signi?cant digits. Work ?

Joules.