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For a cube, what portion of its volume lies within an inscribed sphere? In other words, given a cube of edge=X and a sphere of diameter=X, what's the difference
by CWuestefeld 15y ago
For a cube, what portion of its volume lies within an inscribed sphere? In other words, given a cube of edge=X and a sphere of diameter=X, what's the difference in volume?
Of course, this doesn't begin to account for the vectors, and it assumes that the density is uniform. But it should give us a sense of how much of the gravitational pull differs from our simplistic model.
- T-hawk 15y agoEasier to figure using the radius rather than the diameter. Volume of the sphere is 4pi/3 * r^3, volume of the cube is (2r)^3. Factor out r^3 and you get (4pi/3)/8, or 52% of the cube's volume is within the sphere.
- masterzora 15y agoThe math on that is easy. The volume of a cube is X^3, the volume of a sphere is 1/6 * pi * X^3, so the difference is a little under 1/2 X^3. Put another way, the cube is (roughly) twice the volume of the sphere.