1.

The areas of three adjacent faces of a cuboid are x, y, and z. If the volume is V, prove that V2 = xyz.

Answer»

Given,

Areas of three faces of cuboid = x, y, z

Let length of cuboid = l, breadth = b,height = h

So,

 = x = l x b

= y = b x h

= z = h x a

Or we can write ,

= xyz = l2b2h2 ... ... ... ... . . .(i)

If ‘V’ is volume of cuboid = V = lbh

= V2 = l2b2h2 = xyz ... ... ... ... ... .from (i)

= V2 = xyz Proved


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