Final answer:
The work required to pump half the water over the top of the tank is approximately 4,717,250 J.
Step-by-step explanation:
To calculate the work required to pump half the water over the top of the tank, we need to find the volume of water in the tank and then calculate the work done to raise that volume to the top of the tank. The volume of a cylinder is given by the formula V = πr2h, where r is the radius and h is the height. For this tank, the radius is half the diameter, so r = 3 m. The height of the tank is 6 m. Substituting these values into the formula, we get V = π(3 m)2(6 m) = 54π m3. Half of this volume is 27π m3. The work done is given by the formula W = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height the water is lifted. The density of water is 1000 kg/m³, so the mass is given by m = Vd, where d is the density. Substituting the values, we have m = 27π m3 * 1000 kg/m³ = 27000π kg. The acceleration due to gravity is approximately 9.8 m/s². The height the water is lifted to is 6 m. Substituting these values into the formula, we can calculate the work required: W = (27000π kg)(9.8 m/s²)(6 m) = 1501200π J = 4,717,250 J (rounded to the nearest whole number). Therefore, the work required to pump half the water over the top of the tank is approximately 4,717,250 J.