To find the area of the section of the pool that is blocked off (a sector of a circle), we can use the formula for the area of a sector:
\[ A = \frac{\theta}{360} \times \pi r^2 \]
where \( \theta \) is the central angle in degrees, and \( r \) is the radius of the circle.
- First, we need to find the radius of the pool. Given the diameter is 18 ft, the radius \( r \) is:
\[ r = \frac{18}{2} = 9 \text{ ft} \]
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The angle \( \theta \) is given as \( 75^\circ \).
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Plug these values into the area formula:
\[ A = \frac{75}{360} \times \pi (9^2) \]
Calculating \( 9^2 \):
\[ 9^2 = 81 \]
Now substituting this back into the area formula:
\[ A = \frac{75}{360} \times \pi \times 81 \]
We can simplify \( \frac{75}{360} \):
\[ \frac{75}{360} = \frac{75 \div 15}{360 \div 15} = \frac{5}{24} \]
So now we have:
\[ A = \frac{5}{24} \times \pi \times 81 \]
Calculating that:
\[ A = \frac{405}{24} \pi \]
Now simplifying \( \frac{405}{24} \):
\[ \frac{405 \div 405}{24 \div 405} = \frac{16.875}{1} \text{ (approx.)} \]
So,
\[ A = 16.875 \pi \text{ ft}^2 \]
Thus, the area of the section that is blocked off is:
\[ \boxed{16.875\pi \text{ ft}^2} \]
This matches the response option provided, which is correct.