Faces diagonals

If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), find the cuboid volume.

Solve for x=1.3, y=1, z=1.2

Correct answer:

V =  0.4996

Step-by-step explanation:

x=1.3 y=1 z=1.2  x2=a2+b2 y2=b2+c2 z2=a2+c2  a2=x2−b2=x2−y2+c2=x2−y2+z2−a2 2a2=x2−y2+z2  a=2x2−y2+z2​​=21.32−12+1.22​​≐1.032  … b=2x2+y2−z2​​=21.32+12−1.22​​≐0.7906  … c=2−x2+y2+z2​​=2−1.32+12+1.22​​≐0.6124  V=a⋅ b⋅ c=1.032⋅ 0.7906⋅ 0.6124=0.4996

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