A spherical tank with 4 m radius is full of water. Calculate the work (in Joules) is needed to pump all of the water out if the water exits

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A spherical tank with 4 m radius is full of water. Calculate the work (in Joules) is needed to pump all of the water out if the water exits through a spout that is 2 meters from the top of the tank. The density of water is 1000kg/m3 , the gravity force is 9.8m/s2.

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  1. Answer:

    1,075,536Joules

    Explanation:

    Work is said to be done when an applied force causes an object to cover a distance.

    Workdone = Force × Distance

    Before we can get the force needed to pump all the water out, we need to calculate the mass of water.

    Density = Mass/volume

    Mass = Density × volume

    Given density of water = 1000kg/m³

    Volume of the spherical tank = 4/3πr³

    If radius = 4m

    Volume of the tank = 4/3π(4)³

    = 4/3π × 64

    = 27.16m³

    Mass = 1000×27.16

    Mass = 27,160kg

    Force = mg = 27,160×9.8

    Force = 537,768N

    work (in Joules) needed to pump all of the water out if the water exits through a spout that is 2 meters from the top of the tank will be;

    Work = 537,768×2

    Work = 1,075,536Joules

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