9. In a rectangular parallelepiped $P$ the length of the diagonal is $\sqrt{133}$ and the total surface area is 228. Knowing that one of the sides is the mean proportional between the other two, the volume of $P$ is
(A) 64
(B) 125
(C) 192
(D) 216
(E) 343.
9. The answer is (D). If we denote by $x, y$ and $z$ the lengths of the sides in increasing order, the hypotheses translate to

$$
\left\{\begin{array}{l}
x y + x z + y z = \frac{228}{2} = 114 \\
x^{2} + y^{2} + z^{2} = 133 \\
x z = y^{2}
\end{array}\right.
$$

From the first two, we get $(x + y + z)^{2} = (x^{2} + y^{2} + z^{2}) + 2(x y + x z + y z) = 361$ and thus $x + y + z = 19$. Substituting the third into the first, we get $y(x + y + z) = x y + x z + y z = 114$, from which $y = 6$. Therefore, the volume is $x y z = y^{3} = 216$. On the other hand, a parallelepiped with sides $x = 4, y = 6, z = 9$ satisfies the hypotheses.