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24 January, 20:06

An 18-meter-tall cylindrical tank with a 4-meter radius holds water and is half full. Find the work (in mega-joules) needed to pump all of the water to the top of the tank. (The mass density of water is 1000 kg/m3. Let g = 9.8 m/s2.

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  1. 24 January, 23:06
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    W = mgh

    W = 226290 x 9.8 x 9

    W = 19958778Joules

    W = 19.958778MegaJoules

    Step-by-step explanation:

    Work to full the tank is

    W = mgh.

    m is the mass of the water.

    But density = mass/volume, where volume is the volume of the complete the remaining half full of water to fill the cylindrical tank.

    mass = density x volume.

    Volume of cylinder = πr2h

    Volume to fill the cylinder = (πr2h) / 2. (half of total volume)

    Volume = (22x4x4x9) / (7x2). Height used is 18/2 = 9m

    Volume = 226.29m3.

    Mass = density x volume = 1000 x 226.29 = 226290kg

    Therefore, the work is

    W = mgh

    W = 226290 x 9.8 x 9

    W = 19958778Joule = 19.958778MegaJoules
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