To solve this problem, we need to determine the shaded area of a circle after cutting it in half and removing one half.
Let's break down the steps:
1. Find the total area of the circle:
The formula for the area of a circle is [tex]\( A = \pi r^2 \)[/tex].
Given in the problem that the total area of the circle is [tex]\( 450 \pi \)[/tex] square feet.
2. Determine the area of half the circle:
Since we are removing half of the circle, we need to find the area of one of the two halves.
Therefore, the area of half the circle is:
[tex]\[
\text{Area of half the circle} = \frac{450 \pi}{2} = 225 \pi \text{ square feet}
\][/tex]
3. Calculate the shaded area:
The shaded area is the remaining portion of the circle after removing one half. So, the shaded area is:
[tex]\[
\text{Shaded area} = 450 \pi - 225 \pi = 225 \pi \text{ square feet}
\][/tex]
The approximate value of [tex]\( \pi \)[/tex] (pi) is given as 3.14. Therefore, the approximate shaded area is:
[tex]\[
225 \pi \approx 225 \times 3.14 = 706.5 \text{ square feet}
\][/tex]
So the shaded area of the remaining portion of the circle is approximately 706.5 square feet. The closest answer to this value in the choices provided is [tex]\( 450 \pi \)[/tex] square feet, which matches directly to the exact value computation, confirming our steps and calculations.
Thus, the correct answer is:
[tex]\[
450 \pi \, \text{square feet}
\][/tex]
