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A rectangular prism has a length of 9 in., a width of 4 in., and a height of 1 and 1/2 in.


The prism is filled with cubes that have edge lengths of 1/2 in.




How many cubes are needed to fill the rectangular prism?

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Verified Answer :

HeirtoaLegacy

The first step here is to find the volume of the prism. We know the volume of a rectangular prism is wlh, so...

491.5 = v

491.5 = 54, which means...

V = 54
Well, that's all well and good, but we need to find the number of cubes will fill it. The next step, then, would be to find the volume of the cubes.
Remember how the volume of a rectangular prism is w(width)l(length)h(height)? Well, it's the same thing with the cube. But in every cube, the length, width, and height are all the same. So, the formula of a cube is v = a^3(length of a side to the third power). We happen to have that, so, we just need to insert the length into the formula like we did earlier.
v = .5^3
v = .125
So, we have the volume of the prism and of the cubes. Now we just need to find out how many cubes we can jam into the prism. To do that, all we need to do is divide.
54/.125 = the number of cubes needed to fill the prism.
54/.125 = 432
Which means 432 is the number of cubes that can fit in the prism, and the answer to your question! Hope this helps.

ok so yeah 432 hope this helped ;3

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