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If the areas of three adjacent faces of a cuboid are x, y, z respectively, then the volume of the cuboid is :
Answer & Solution
Correct Answer:
Option
C
Let, length = l, breadth = b, height = h
Then,
x = lb, y = bh, z = lh
Let, V be the volume of the cuboid
Then, V = lbh
$$\eqalign{ & \therefore xyz = lb \times bh \times lh \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\left( {lbh} \right)^2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {V^2} \cr & \,\,\,\,\,\,\,\,\,\,\,or\,V = \sqrt {xyz} \cr} $$
Then,
x = lb, y = bh, z = lh
Let, V be the volume of the cuboid
Then, V = lbh
$$\eqalign{ & \therefore xyz = lb \times bh \times lh \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\left( {lbh} \right)^2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {V^2} \cr & \,\,\,\,\,\,\,\,\,\,\,or\,V = \sqrt {xyz} \cr} $$
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