The area of three adjacent faces of a cuboid are p, q and r. The volum – InterviewSolution

1.

The area of three adjacent faces of a cuboid are p, q and r. The volume of cuboid is V. Prove that V2 = pqr.

Answer»

Let l, b and h be the dimensions of cuboid respectively. Then,

p = lb

q = bh

r = hl

∴ pqr = (lb) (bh) (hl)

= l²b²h²

= (lbh)²

= V²

⇒V² = pqr

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