$23 \cdot 26$ If the areas of the side, front, and bottom faces of a rectangular solid are 12 square inches, 8 square inches, and 6 square inches, respectively, then its volume is
(A) 576 cubic inches.
(B) 24 cubic inches.
(C) 9 cubic inches.
(D) 104 cubic inches.
(E) None of the above answers is correct.
(1st American High School Mathematics Examination, 1950)
[Solution] Let the length, width, and height of the rectangular prism be $x, y, z$, respectively. Then the volume of the rectangular prism is
$$
\begin{aligned}
V & =x y z \\
& =\sqrt{x^{2} y^{2} z^{2}} \\
& =\sqrt{x y \cdot y z \cdot z x} \\
& =\sqrt{12 \cdot 8 \cdot 6}=24 .
\end{aligned}
$$

Therefore, the correct choice is (B).