"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.
When a cube is cut by 15 cuts, it can produce a maximum of 27 identical pieces. Each cut can create at most 2 identical pieces, so with 15 cuts, you can get 2 x 15 = 30 pieces. However, 3 of these pieces will be removed as they are the corners of the cube, leaving you with 30 - 3 = 27 identical pieces.
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.
To cut a cube into 504 identical pieces, you would need to make 503 cuts. Each cut divides the cube into two pieces, so the first cut creates 2 pieces, the second cut creates 4 pieces, the third cut creates 8 pieces, and so on. Therefore, to reach 504 pieces, you would need to make 503 cuts.
If a cube of jello is cut into two pieces the density of the pieces do not change.
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.
The density of each piece remains the same as the density of the original gold bar. Density is a characteristic property of a material and does not change with size or shape. Thus, each new piece will have the same density as the original gold bar.
Exactly the same.
If you cut a metal in half, each half will have the same density as the original metal, so the density of each half will still be 8.4. The density of a material does not change when you cut it into pieces.
No, there have never been two pieces of exactly identical popcorn.
No, cutting an object doesn't affect its density. Density is a physical property that remains constant regardless of an object's shape or size. It is determined solely by the mass and volume of the material.
When a cube is cut by 15 cuts, it can produce a maximum of 27 identical pieces. Each cut can create at most 2 identical pieces, so with 15 cuts, you can get 2 x 15 = 30 pieces. However, 3 of these pieces will be removed as they are the corners of the cube, leaving you with 30 - 3 = 27 identical pieces.
It means: * Calculate the density of an object * Calculate the density of its pieces * Compare
9 pieces
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.
Two pieces of wood of different sizes can have the same density if they are made from the same type of wood material and have the same mass-to-volume ratio. Density is calculated by dividing the mass of an object by its volume, so as long as these two pieces have the same density, they will weigh the same for their respective volumes, even though they are different in size.