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Half would be 50% of something. So half of half would be 25% of something.
The volume will be reduced to a half of its original value. If the mass is (approximately) evenly distributed throughout the wooden block then the mass will also reduce to a half of its original value and the density will not change.
Doubling and subtracting 1
No it will not change. Density is mass divided by volume. Since the ratio of the mass is 1/2 and the volume ratio is 1/2, there is no change. The same holds true no matter how you cut the block, as both mass and volume change proportionally the same.
Volume of half a sphere = 2/3*pi*radius3 Volume = 2/38pi*103 = 2094.395102 cubic units