A sphere has a radius 2 inches. Acube fits perfectly inside of the ball such that all 8 corners of the cube?

Question

touch the sphere. What arethe dimensions of the cube?

Answer 1

diameter of sphere, 4, is diagonal of cube, which is √3 times length of side of cube, so

s√3 = 4, s = 4/√3 = (4/3)√3 = 2.3094 in.

Answer 2

the sector can't be a nil dimensional element with the aid of fact it violates situation variety 4 and a million. a nil dimensional element has no length, no width, and no intensity, it would not occupy area hence it may no longer occupy the two time or area. additionally, if that is 0 dimensional then this violates the mathematical ratio of the sector, it somewhat is ?. everywhere on the sector, the ratio of the circumference to the diameter is ? it somewhat is impossible for a nil dimensional element, hence this removes this posit as an evidence. to ensure that the sector to be thoroughly flat we nonetheless can no longer violate this mathematical relation with the aid of fact it particularly is often around. the only way for the sector to be around and flat is that if an merchandise can commute to the left edge and finally end up on the spectacular edge, style of like interior the sport "asteroids" the place the deliver travels alongside a 2 dimensional airplane, yet in no way falls off with the aid of fact it particularly is a 2 dimensional sphere (nicely, the exterior is) and on a sphere you may pass in one direction and finally end up on the comparable element. it particularly is the only way wherein a sphere could nicely be "flat" at any length different than 0 is that if the climate are someway appropriate via an extra length, yet given the circumstances one might degree a curvature to the exterior. So, relative to an outdoors observer the exterior might seem to be flat, yet for all and sundry on the exterior, they might degree a curvature. This sphere is hypothetically existent interior the universe and there is no longer something interior the regulations of physics that denies greater dimensions or greater dimensional passage techniques which includes wormholes that should advantage a 2 dimensional airplane the traits of a sphere. Very exciting question via the way, that is probably the 1st question on right here that made me think of this lots. 10 trillion circumstances greater effective than the "2012" questions approximately right here. is this spectacular?