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Let's solve this problem step by step:

### Given:
- A circle whose diameter is approximately 11 feet.
- A square with side length 8 feet is cut out from the circle.
- We are asked to find the area of the remaining (shaded) portion of the circle.

### Step 1: Find the area of the circle
The formula for the area of a circle is:

\[
A_{\text{circle}} = \pi r^2
\]

The diameter of the circle is 11 feet, so the radius \( r \) is:

\[
r = \frac{11}{2} = 5.5 \text{ feet}
\]

Using \( \pi \approx 3.14 \), the area of the circle is:

\[
A_{\text{circle}} = 3.14 \times (5.5)^2 = 3.14 \times 30.25 \approx 95.585 \text{ square feet}
\]

### Step 2: Find the area of the square
The area of the square is given by:

\[
A_{\text{square}} = s^2
\]

where \( s = 8 \) feet. So,

\[
A_{\text{square}} = 8^2 = 64 \text{ square feet}
\]

### Step 3: Find the area of the remaining portion
The remaining area (shaded region) is the area of the circle minus the area of the square:

\[
A_{\text{shaded}} = A_{\text{circle}} - A_{\text{square}} = 95.585 - 64 = 31.585 \text{ square feet}
\]

### Final Answer:
The approximate area of the remaining shaded region is **31.585 square feet**.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the area of the circle if its diameter is doubled?
2. How would the result change if the square side were increased to 9 feet?
3. What is the radius if the area of the circle is 100 square feet?
4. How does the formula for a circle's area differ from the formula for a square's area?
5. What would the shaded area be if a rectangle, not a square, were cut from the circle?

**Tip:** Always verify that the circle's radius is larger than half the side length of the square when cutting out shapes to ensure proper geometric containment.

A square is cut out of a circle whose diameter is approximately 11 feet. What is the approximate area (shaded region) of the remaining portion of the circle in square feet? (A = πr² where π ≈ 3.14)

This problem involves calculating the shaded region of a circle after a square with a side length of 8 feet is cut out from a circle with a diameter of 11 feet. Learn how to find the area of the circle and the square using the formulas A = πr² and A = s², respectively.

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