A rectangular swimming pool is 20 meters long and 10 meters wide. A circular Jacuzzi with a diameter of 4 meters is placed in the pool. How many square meters is the area of the pool that is not occupied by the Jacuzzi?

We have a rectangle swimming pool with a jacuzzi within it. We are solving for the area of the pool not occupied by the jacuzzi. This is represented in equation form by:

[tex]A_{\text{pool}} = A_{\text{rect}} - A_{\text{jacuzzi}}[/tex]

We can find the areas using the formulas:

[tex]A_{\text{rect}} = l \cdot w[/tex]
[tex]A_{\text{circle}} = \pi r^2[/tex]

Plugging these into the above equation along with the given values, we get:

[tex]A_{\text{pool}} = l \cdot w - \pi r^2[/tex]

[tex]l = 20[/tex]
[tex]w=10[/tex]
[tex]r\ =\ d/2\ =\ 4/2\ =\ 2[/tex]

↓↓↓

[tex]A_{\text{pool}} = 20 \cdot 10 - \pi (2)^2[/tex]

[tex]A_{\text{pool}} = 200 - \pi(4)[/tex]

[tex]\boxed{A_{\text{pool}} = 200-4\pi \text{ m}^2 \ \approx\ 187.4\text{ m}^2 }[/tex]

So, the area of the pool not occupied by the jacuzzi is approximately 187.4 m².