"Wood" may not be uniform and homogeneous ... there may be knots, voids, rough grain, etc.
So it's a poor choice of material to illustrate the important principle here.
The principle is: Provided the sample is homogeneous, like plastic or a refined metal, every piece of it,
no matter how large or small, has the same density. Density is a property of the substance, without
any reference to the shape or size of the sample.
If the block is cut into pieces, no matter how many, and no matter whether they're the same size or
different sizes, every piece should have the same density as the aggregate block had before it was cut.
equal the density of any other piece, assuming that the original cube was made of the same uniform substance.
In one sense you cannot. The cakes would have a different number of faces which were part of the original faces. To that extent the pieces will not be identical. If such pieces are considered identical, and if the cake pieces can be stacked before cutting, then 9 cuts will suffice. Without stacking, 12 cuts are required. If the cake can be stacked and cut, and a little wastage (less than 2.5%) is pemitted, then 7 cuts will be enough.
21 cuts required to cut a cube into 504 identical pieces.
If a cube of jello is cut into two pieces the density of the pieces do not change.
216
The density of cutted pieces is identical; of course this is valid only for a homogeneous material.
equal the density of any other piece, assuming that the original cube was made of the same uniform substance.
No. If an object is homogeneous, then you can cut it up into a bazillion smaller pieces, and every piece has the same density as the original object had.
Exactly the same.
Exactly the same.
No, there have never been two pieces of exactly identical popcorn.
It means: * Calculate the density of an object * Calculate the density of its pieces * Compare
9 pieces
You are confusing density with weight. Two pieces of wood of the same density but different sizes have different weights. Density, you could say, is like hardness. If you take a 6 foot piece of wood, and cut 2 feet from it, the two pieces of wood are definitely different weights but the same hardness. Since they came from the same original piece of wood, they almost have to be the same density. There are some types of wood that have such high density that they will not float on water.
In one sense you cannot. The cakes would have a different number of faces which were part of the original faces. To that extent the pieces will not be identical. If such pieces are considered identical, and if the cake pieces can be stacked before cutting, then 9 cuts will suffice. Without stacking, 12 cuts are required. If the cake can be stacked and cut, and a little wastage (less than 2.5%) is pemitted, then 7 cuts will be enough.
21 cuts required to cut a cube into 504 identical pieces.
Yes, a crayon has greater density than pieces of crayon, assuming the pieces are not heated and mashed together. That's because the crayon has density X and air has a lower density Y. Some combination of X and Y will always be less than X.