## 33. Reservoir

The reservoir has the shape of a rectangular parallelepiped, the width of which is half the length. It is filled to three eighths of its height. When 76 hl [1 hl (hectoliter) = 0.1 m³] is added, the water level rises by 0.38 m. After this, two sevenths of the reservoir remain to be filled.

What is the height of the reservoir?
33. As units of measurement, we will choose meters, square meters, and cubic meters.

Let $x$ be the desired height, and $y$ be the width of the reservoir. Then the length of the reservoir is $2 y$, and therefore, the area of the base is $2 y^{2}$; hence, the increase in the volume of water by 76 hl can be expressed as:

$$
0.38 \cdot 2 y^{2} = 76 / 10
$$

From this, $y^{2} = 10, y = \sqrt{10}$.

But after adding 76 hl, the reservoir, which was initially filled to three eighths, ended up filled to five sevenths. Therefore,

$$
(5 / 7 - 3 / 8) 2 y^{2} x = 7.6 \text{, }
$$

or

$$
x = \frac{7.6}{2 \cdot 10 \cdot (5 / 7 - 3 / 8)}
$$

i.e., $x \approx 1.12 \text{ m}$.

Thus, the height of the reservoir is approximately 1.12 m.