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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 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
= 225 cm^6.
It gives the volume of the cuboid, after taking square root of both sides
xyz = = 15 cm^3.
ANSWER. The volume of the cuboid is 15 cm^3.
Solved.