Faces diagonals

Find the cuboid volume if the cuboid's diagonals are x, y, and z (wall diagonals or three faces).

Solve for x=1, y=1.1, z=1

Correct answer:

V =  0.3802

Step-by-step explanation:

x=1 y=1.1 z=1  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​​=212−1.12+12​​≐0.6285  … b=2x2+y2−z2​​=212+1.12−12​​≐0.7778  … c=2−x2+y2+z2​​=2−12+1.12+12​​≐0.7778  V=a⋅ b⋅ c=0.6285⋅ 0.7778⋅ 0.7778=0.3802

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