SOLUTION: Hi A cuboid has front,side and top faces of areas 10a cm^2 7.5a cm^2 and 3cm^2 respectively. What is the volume of the solid in cm^2. Thanks

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Question 1205448: Hi
A cuboid has front,side and top faces of areas 10a cm^2 7.5a cm^2 and 3cm^2 respectively. What is the volume of the solid in cm^2.
Thanks
Answer by ikleyn(52821) About Me  (Show Source):
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A cuboid has front side and top faces of areas 10 cm^2, 7.5 cm^2 and 3cm^2, respectively.
What is the volume of the solid in highlight%28cross%28cm%5E2%29%29 cm^3.
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Let x, y, z be three dimensions of the cuboid.


From the condition, we have

    xy = 10   cm^2,    (1)

    yz =  7.5 cm^2,    (2)

    xz =  3   cm^2.    (3)


Multiply equations (1), (2) and (3).  You will get

    x^2*y^2*z^2 = 10*7.5*3 = 225 cm^6.


Thus we have  

    %28xyz%29%5E2 = 225  cm^6.


It gives the volume of the cuboid, after taking square root of both sides

    xyz = sqrt%28225%29 = 15 cm^3.


ANSWER.  The volume of the cuboid is 15 cm^3.

Solved.