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25 Sep 2019, 21:47
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A sphere, diameter 6, is cut to form a cube. What is the maximum possible distance between two vertices after the cut?
A. \(3\)
B. \(3\sqrt{2}\)
C. \(2\pi\)
D. \(6\)
E. \(3(\pi-2)\)
25 Sep 2019, 22:28
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We can look at this question as a square inscribed within a circle. Since the edges of the square will touch the circle, then the diagonal is equal to the diameter of the circle. And by this extension, the maximum possible distance between any two edges if a cube is cut out of a sphere will be equal to the diameter of the sphere.
Since we know that the diameter of the sphere is 6 units, then the maximum distance between the vertices will be 6 units as well.
The answer is therefore D.
Since we know that the diameter of the sphere is 6 units, then the maximum distance between the vertices will be 6 units as well.
The answer is therefore D.
25 Sep 2019, 23:56
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A sphere, diameter 6, is cut to form a cube. What is the maximum possible distance between two vertices after the cut?
Since a cube with side ‘a’ has longest distance equal to √3a, all the vertices of the cube cut out from a sphere of diameter 6 would touch the sphere’s surface such that cube is of largest size.
Hence √3a = 6.
Answer (D).
Since a cube with side ‘a’ has longest distance equal to √3a, all the vertices of the cube cut out from a sphere of diameter 6 would touch the sphere’s surface such that cube is of largest size.
Hence √3a = 6.
Answer (D).
