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horsena [70]
3 years ago
13

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 c

ube to the surface of the sphere?
Mathematics
1 answer:
DedPeter [7]3 years ago
8 0

Answer:

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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Pythagoras theorem is a basic relationship in geometry between the three sides of a right triangle.

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