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12 August, 11:40

A concrete beam is used as a counterweight. The beam is 6 feet long with an 8-inch by 8-inch square base. If the beam has to be replaced by bags of sand, what is the volume (in ft^3) of the sand that will have the same weight as the beam?

Use the following densities for the materials involved (in pounds per cubic foot):

concrete 150

sand 100

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  1. 12 August, 11:55
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    4 cubic feet

    Step-by-step explanation:

    Step 1:

    Length of the concrete beam = 6 feet

    Side for the square base = 8 inch = 8/12 feet

    So, volume of the concrete beam = 6 * (8/12) * (8/12) = 2.67 cu ft

    Hence mass of the beam = density of the beam * volume

    = 150 * 2.67 = 400 kg

    Step 2:

    we need the the weight of sand equivalent to the concrete beam.

    Mass of the sand bags = den of sand * vol

    => 100 * volume of sand = 400

    => Volume of sand = 400/100 = 4 cu feet.
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