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I see your point Fig, but i still don't see why the other side should be 10/2*sqrt(2), where does the sqrt(2) come from?
If the sphere is inscribed then, it is touching the sides of the cube in the middle so the 2 sides of the right angle should be identical.
I see your point Fig, but i still don't see why the other side should be 10/2*sqrt(2), where does the sqrt(2) come from? If the sphere is inscribed then, it is touching the sides of the cube in the middle so the 2 sides of the right angle should be identical.
Appreciate your further explanation, thanks!!!
As u said, the contact point of the sphere is the center (gravity point) of a scare side. But, the distance is not the radius.
Actually, we can use the fact that the lenght of a line joining 2 opposite vertex on a same scare side is defined by hyp^2=10^2 + 10^2 => hyp = 10*sqrt(2).
Thus, to have the distance from 1 vertex to the contact point of the sphere at the center of a side, we divid by 2: hyp/2 = 10*sqrt(2)/2 = 5*sqrt(2)
The most simple is to draw 1 side of the cube... then, u can notice that each side measure 10.
I don't understand that last answer, so maybe it's right.
Anyway, here's my solution.
Imagine the cube sitting with one corner at the origin and another corner at (10, 10, 10). The distance from these two points is the distance of the long diagonal. The distance formula says that this distance is Sqrt((10 - 0)^2 + (10- 0)^2 + (10-0)^2) = Sqrt(3*10^2) = 10*Sqrt(3).
The sphere sitting inside the cube has diameter 10. Since a sphere in a cube is completely symmetric, the distance from a vertex to the sphere is the same for all vertices. So along that long diagonal we run through the middle of the sphere. The distance outside the sphere is 10*Sqrt(3) - 10. The distance from one vertex to the sphere must be half that by symmetry. So the answer is 1/2*(10*Sqrt(3) - 10) = 5*(Sqrt(3) - 1)