Question 611580
Two vertices of a cube have coordinates A(5,12,12) and B(20,28,24). What is the smallest possible volume of the cube?
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A and B can be on the same edge, diagonally on the same face, or diagonally thru the center of the cube.
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The distance AB is
{{{sqrt(diffx^2 + diffy^2 + diffz^2) = sqrt(15^2 + 16^2 + 12^2) = sqrt(625)}}}
AB = 25
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If AB is an edge, volume = 25^3 = 15625
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If AB is a diagonal on a face, the edges are 5sqrt(2)/2 --> Vol =~ 44.19
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If AB is a diagonal thru the center, the edges are 5sqrt(3)/3 --> Vol =~ 24.056