To solve this problem, we need to calculate the area of the shaded region. Here’s the step-by-step solution:

Step 1: Understand the Problem

• A circle with radius 16 feet is inscribed in a square.
• We are asked to find the area of the shaded region, which is the area outside the circle but inside the square.
• Use 3.14 for π.

Step 2: Calculate the Area of the Circle

The area $A$ of a circle is given by the formula: $A_{\text{circle}} = \pi r^2$ where $r = 16$ feet.

Using 3.14 for $\pi$: $A_{\text{circle}} = 3.14 \times (16)^2$ $A_{\text{circle}} = 3.14 \times 256$ $A_{\text{circle}} = 804.64 \text{ square feet}$

Step 3: Calculate the Area of the Square

Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square. The diameter $D$ of the circle is: $D = 2 \times r = 2 \times 16 = 32 \text{ feet}$ So, the side length of the square is 32 feet.

The area $A$ of a square with side length $s$ is given by: $A_{\text{square}} = s^2$ $A_{\text{square}} = 32^2$ $A_{\text{square}} = 1024 \text{ square feet}$

Step 4: Calculate the Area of the Shaded Region

The shaded region is the area of the square minus the area of the circle: $A_{\text{shaded}} = A_{\text{square}} - A_{\text{circle}}$ $A_{\text{shaded}} = 1024 - 804.64$ $A_{\text{shaded}} \approx 219.36 \text{ square feet}$

Step 5: Find the Closest Answer

The closest answer to 219.36 square feet is: D.) 220.16 square feet

Final Answer:

The correct answer is: D.) 220.16 square feet

Would you like more details or have any questions?

Related Questions:

1. How would the answer change if the radius of the circle were different?
2. What if the square were not perfectly inscribed? How would we calculate the shaded area?
3. How does changing the value of $\pi$ affect the solution?
4. How do we find the area of shaded regions in more complex shapes?
5. What if the circle was outside the square instead of inside it?

Tip:

Remember that for inscribed shapes, the diameter of the circle equals the side length of the square. This simplifies many calculations!