Sorry, i couldnt figure out how else to post this problem than to attach the image
why is the answer not E ?[/img]
why is the answer not E ?[/img]
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It can be derived from Pythagoras' Theorem that the length of the diagonal in a cuboid of edge lengths a,b and c is (a^2 + b^2 + c^2)^0.5.
For a cube, since all the edges are equal, the length of a diagonal for edge length 'a' is a(3)^0.5.
So, for a edge length 10, the length of the diagonal is 10(3)^0.5.
If you draw a cube with a sphere completely inscribed in it, you will see that the diameter of the sphere = edge of the cube and
The Shortest possible distance from one vertex to surface of sphere = Half of (length of diagonal - diameter of spehere)
= 1/2*(10(3)^0.5 - 10)
= 5(3)^0.5 - 5
(D) is the answer
