Problem 1. The areas of the sides of a cuboid are 16, 20, and 45. Calculate the volume of the cuboid.
Solution. Let the sides of the cuboid be denoted by $a, b$, and $c$. Then from the condition of the problem, we get $a b=16, a c=20$ and $b c=45$. By multiplying the three equations, we obtain $a^{2} b^{2} c^{2}=16 \cdot 20 \cdot 45=14400$ (7) from which we find $V=a b c=\sqrt{14400}=120$.