Question 1 (5 marks). A spherical tank with a radius of 3 metres is half full of water as shown in Figure 1. It has a spout of length 1 metre sticking out from the top of the tank. Find the work required to pump all the water in the tank out of the spout. Assume work is measured in newton-meters. FIGURE 1. The side view of the tank. Solution ! 06 / 04 / 24 The weight density of the water = 8 = 9800 N / M 2 Radial r = 3 m Spout length 4 = Im . From pythagoras theanen 22+42= 82 T The radius of the strip = ( = 2 1 9 - 921 ) Area of the atrip = IN2 2 1 [9 -82] The Volume of Atrip ? 1 x [ 9 - 9 2 ] x dy py PL . 8 = m The weight of the strip = 9 8 0 0 x x x 9 - g z J x dy The height to be moved = 4 - 4 6 = I Coarkdone = [ F (g ) . H ( y ) dy asdoepo.o 5 (2)0) = [ ( 4 - y ) x 9 8 0 0 x x x [ 9 -g 2 ] x dy 20 . 0 3