The areas of three adjacent faces of a cuboid are x, y and z. If the v

1.	The areas of three adjacent faces of a cuboid are x, y and z. If the volume is v, prove that y2 = xyz.
Answer» Let l, b and h be the length, breadth and height of a cuboid. Volume of cuboid = v = l x b x h = lbh …(1) Since x, y and z represent areas of three adjacent faces of the cuboid, then x = lb, y = bh, z = lh => xyz = (lb) x (bh) x (hl) => x × y × z = l² x b² x h² => xyz = (l x b x h)² => xyz = v² Hence v² = xyz

The areas of three adjacent faces of a cuboid are x, y and z. If the volume is v, prove that y2 = xyz.

Answer»

Let l, b and h be the length, breadth and height of a cuboid.

Volume of cuboid = v = l x b x h = lbh …(1)

Since x, y and z represent areas of three adjacent faces of the cuboid, then

x = lb, y = bh, z = lh

=> xyz = (lb) x (bh) x (hl)

=> x × y × z = l² x b² x h²

=> xyz = (l x b x h)²

=> xyz = v²

Hence v² = xyz

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The areas of three adjacent faces of a cuboid are x, y and z. If the volume is v, prove that y2 = xyz.

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