For Q13-Q14, consider a rectangular parallelepiped O A C ′ B A ′ C B ′ O ′ with O A = 2 , OB = 3 , OC = 4 . If the areas of triangles OPQ , OQR , OPR are least as in the construction, find the volume

Question

For Q13-Q14, consider a rectangular parallelepiped O A C ′ B A ′ C B ′ O ′ with O A = 2 , OB = 3 , OC = 4 . If the areas of triangles OPQ , OQR , OPR are least as in the construction, find the volume of tetrahedron OPQR .

TestHub · Accepted Answer

Minimizing the three triangular areas gives OP = 4 , OQ = 6 , OR = 8 along mutually perpendicular axes. Thus volume = 6 1 ​ ( 4 ) ( 6 ) ( 8 ) = 32 .

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