cube with side-length "b": find formula for number of blocks

mathproblemssss

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*picture of a cube with b posted on the lenghth, width, & heighth*

5. write an expression representing the total number of blocks packaged in a cube measuring b blocks on one edge.

6. the team decides to take one layer of blocks off the top of the package. write an expression representing the number of blocks in the top layer of the package.

7. The team finally decides that their facorite package arrangement is to take 2 layers of blocks off the top or a cube measuring b blocks along one edge. write an expression representing the number of blocks left behing after the top two layers are removed.
 
Re: confused with volume. please help.

my trouble is that i get lost when they start knocking off layers.
please help.
 
Re: confused with volume. please help.

I think you would first have to know the dimensions of the blocks you are packing in the cube - unless you were just assigning a variable for the blocks' dimensions.
 
Re: confused with volume. please help.

Oh, okay I get it, so the expression for the number of blocks would be b^3, right?
 
Re: confused with volume. please help.

yes, i believe number 5 is b cubed because that is the formula for volume. but then they knowck of a layer, so one of the measurements couldnt still be B.
 
Re: confused with volume. please help.

So if you knock off the top layer, the number of cubes not in the top layer would be:

(b-1)*(b)*(b)


right? so that means the number of cubes in the top layer you knocked off would be the total number of cubes (b^3) minus the number of cubes left (the formula we just figured out>>>>>> (b-1)*(b)*(b) )
So:

b^3 - [(b-1)*(b)*(b)]
or
b^3 - [(b-1)*b^2] = number of cubes in the top layer
 
Re: confused with volume. please help.

For 7 it would be the same concept as 6, except 2 layers are taken off the height so:

(b-2)*(b)*(b)

I think... hope I helped!
 
Re: confused with volume. please help.

For part 6, I got [(b-1)*(b)*(b)] from:

height*length*width

The height would be (b-1) because you're knocking off the top layer and like you said it could still be b and obviously, (b) and (b-1) aren't equal! The width (b) and the length (b) would be the same though:

(b-1)*(b)*(b)
 
Re: confused with volume. please help.

Haha - I'm guessing that means you got it; my pleasure!
 
Re: confused with volume. please help.

sgtpepper said:
b^3 - [(b-1)*b^2] = number of cubes in the top layer


Each layer is made up of b^2 cubes because each layer forms a b by b grid.

b^3 - [(b-1)*b^2] simplifies to b^2.

Cheers,

~ Mark :)
 
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