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19 May, 16:57

14. 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?

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  1. 19 May, 17:38
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    5 (√3 - 1)

    Step-by-step explanation:

    Edge of cube = 10

    If the sphere is inscribed in a cube, the edges of the cube is equal to the diameter of the sphere.

    Diameter = 10

    We will then find the diagonal of the cube.

    Diagonal = √10^2 + 10^2 + 10^2

    = √300

    = 10√3

    Let X be the distance between the vertex of the cube and the surface of the sphere

    X = (diagonal - diameter) / 2

    X = (10√3 - 10) / 2

    X = (10 (√3 - 1)) / 2

    X = 5 (√3 - 1)
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