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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?

 Jan 15, 2020
 #1
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The shorrtest distance is 10 - 5*sqrt(2).

 Jan 15, 2020
 #2
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*****

 

 

cool cool cool

 Jan 15, 2020
edited by CPhill  Jan 15, 2020
 #3
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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?

 

laugh

 Jan 15, 2020
 #4
avatar+36916 
+2

Distance from center to corner (vertice) = sqrt (5^2 + 5^2 + 5^2) = sqrt 75

 

distance from center to surface is 5

sqrt75 - 5 = 3.66 units

 Jan 15, 2020

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