GmatKiss wrote:A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?
10( root(3)- 1)
5
10( root(2)- 1)
5( root(3)- 1)
5( root(2)- 1)
Explain pls!
I received a PM asking me to clarify the solution.
The formula for the diagonal of a cube = √(3e²).
In the figure above, x = the distance between the cube and the surface of the sphere.
The diagonal of the cube = 2x + the diameter of the sphere.
Thus, x = (diagonal of the cube - diameter of the sphere)/2.
The diagonal of the cube = √(3e²) = √(3*10²) = 10√3.
The diameter of the sphere = the edge of the cube = 10.
Thus, x = (10√3 - 10)/2 = 5√3 - 5 = 5(√3 - 1).
The correct answer is
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