King Original I. designed and had a pool built himself. In the picture, you can see what it looks like from above. The bottom is covered with square tiles with a side length of 2 meters, the concrete walls are 3 meters high and 0.5 meters thick. Find out how many kilograms of concrete were used for the pool walls if $1 \mathrm{~m}^{3}$ of concrete weighs $2000 \mathrm{~kg}$.

( $S$. Bednářová)

![](https://cdn.mathpix.com/cropped/2024_04_17_e148e2850cb5b4728907g-2.jpg?height=346&width=722&top_left_y=1943&top_left_x=701)
In the following image, the "division" of concrete into individual parts is indicated. In the "outer corners," dark squares are marked, and in the "inner corners," squares with the number 2 are marked. Both types of squares have the same area.

![](https://cdn.mathpix.com/cropped/2024_04_17_e148e2850cb5b4728907g-3.jpg?height=437&width=919&top_left_y=204&top_left_x=594)

We want to calculate the volume of the pool walls. Imagine that we place the individual walls side by side. This way, we get one large wall in the shape of a rectangular prism. The height of this prism (the same as the height of the pool) is 3 meters. The remaining dimension is obvious; it is the width of the wall, which is 0.5 meters. We need to determine the total length. The total length is the perimeter of the pool increased by the "outer" corners (there are 10 in total) and decreased by the "inner" corners (there are 6 in total). We subtract because each "inner" corner is counted twice in the perimeter.

Now we can easily calculate that the total length is

$$
32 \cdot 2 \mathrm{~m} + 10 \cdot 0.5 \mathrm{~m} - 6 \cdot 0.5 \mathrm{~m} = 66 \mathrm{~m}.
$$

The rectangular prism has dimensions (in meters) $66 \times 3 \times 0.5$, so it weighs

$$
66 \cdot 3 \cdot 0.5 \cdot 2000 \mathrm{~kg} = 198000 \mathrm{~kg}.
$$

Therefore, $198000 \mathrm{~kg}$ of concrete was used for the construction of the pool.