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

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.