A cuboid having surface areas of 3 adjacent faces a,band c has volule?

1.	A cuboid having surface areas of 3 adjacent faces a,band c has volule?
Answer» Volume=(abc)^1/2 In the given solution replace x.y.z with a,b,cLet the length, breath and height of the cuboid be\xa0l\xa0units,\xa0b\xa0units and\xa0h\xa0units respectively.Given, area of three adjacent faces of the cuboid are\xa0x,\xa0y\xa0and\xa0z\xa0square units.Area of the face ABEF =\xa0l\xa0×\xa0b\xa0=\xa0x ...(1)Area of the face ABCD =\xa0l\xa0×\xa0h\xa0=\xa0y ...(2)Area of the face ADGF =\xa0b\xa0×\xa0h\xa0=\xa0z ...(3)Multiplying (1), (2) and (3), we get(l\xa0×\xa0b) × (l\xa0×\xa0h) × (b\xa0×\xa0h) =\xa0x\xa0×\xa0y\xa0×\xa0z∴\xa0l2\xa0b2\xa0h2\xa0=\xa0x y z ...(4)Volume of the cuboid =\xa0l\xa0×\xa0b\xa0×\xa0h∴\xa0V\xa0=\xa0l b hSquaring on both sides, we getV\xa02\xa0=\xa0l2\xa0b2\xa0h2∴\xa0V\xa02\xa0=\xa0xyz \xa0[Using (4)]

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