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?

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)

because they could drop even lower..