Minimum Distance between surface of sphere and cube

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SUMMARY

The minimum distance between the surface of a sphere with a radius of 3 and center at (2,1,2) and a cube with a side length of 6 centered at (12,11,12) is determined by calculating the distance from the sphere's center to the nearest point on the cube. The initial approach of finding the distance between the centers is incorrect; instead, the distance from the sphere's center to the cube's surface must be calculated, and then the sphere's radius should be subtracted from that distance to find the minimum distance to the sphere's surface.

PREREQUISITES
  • Understanding of 3D geometry concepts
  • Familiarity with the sphere equation: (x-x0)^2+(y-y0)^2+(z-z0)^2=r^2
  • Knowledge of distance calculation between points in 3D space
  • Basic understanding of cube geometry and its spatial properties
NEXT STEPS
  • Calculate the distance from a point to a cube in 3D space
  • Explore methods for finding the nearest point on a geometric shape
  • Review sphere and cube intersection problems in computational geometry
  • Study optimization techniques for distance calculations in 3D environments
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Students studying geometry, mathematicians working on spatial problems, and anyone interested in computational geometry and optimization techniques.

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Homework Statement


Find the minimum distance between the surface of a sphere with radius 3 with center (2,1,2) and a cube with length 6 with center (12,11,12)


Homework Equations


sphere formula: (x-x0)^2+(y-y0)^2+(z-z0)^2=r^2


The Attempt at a Solution


Don't know how to attempt this problem. My assumption is to find the distance between the two centers, then subtract the distance between the radius and the surface of the sphere, and also subtract the distance between the center of the cube to one of the sides. would this procedure be correct?
 
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Your procedure is partially correct... but you will want to find the minimum distance between the center of the sphere and a point on the cube. (not the distance between the centers)
then you will just subtract the radius from that number
 
Last edited:

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