3 $[\quad$ Volume of a parallelepiped $\quad]$

The base of a right parallelepiped is a parallelogram, one of the angles of which is $30^{\circ}$. The area of the base is 4. The areas of two lateral faces of the parallelepiped are 6 and 12. Find the volume of the parallelepiped.
Let $a$ and $b$ be the sides of the parallelogram, $c$ be the height of the parallelepiped, and $V$ be its volume. From the problem statement, we have:

$$
a b \sin 30^{\circ}=\frac{1}{2} a b=4, a c=6, b c=12
$$

Therefore,

$$
a b c 2=6 \cdot 12=72, c 2=\frac{\frac{T 2}{\alpha b}}{\alpha i}=\frac{72}{8}=9
$$

from which $c=3$. Therefore,

$$
V=\frac{1}{2} a b c=4 \cdot 3=12 .
$$

## Answer

12.00