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How much metal is needed to cast a cubical metal box with outer side 10 inches long if the thickness of its walls should be exactly 2 inches?

Respuesta :

notice the picture below

so...  a cube has all sides equal, so is just a rectangular prism with equal sides
and a rectangular prism is just 6 rectangles stacked up to each other at the edges

now, notice in the graph at the bottom, one of the rectangles with a thickness of 2inches

so... just get the volume of each, and add them up, that's how much metal is needed
Ver imagen jdoe0001

You can use the difference of volume of the outside cube with the inside cube to get the volume of the metal used.

The amount of metal needed for the given condition is

How to get the volume of wall of some closed figure if the width of the walls are significant?

There will  be two figures. First outside and first inside. Supposing that the figure is made end to end with only one layer, we have:

Volume of the walls needed for the figure = Volume of the outer figure - volume of the internal figure

Using above conclusion

We have:

length of side of cube outside = 10 inches

length of side of cube internally = 10 - 2 = 8 inches

Volume of wall = Volume of outer cube - volume of internal cube

Amount of metal needed = volume of wall = [tex]10^3 - 8^3 = 1000 - 512 = 488 \: \rm inch^3[/tex]

Thus, the amount of metal needed  is 488 cubic inches.

Learn more about volume here:

https://brainly.com/question/26136041

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