Questions: A square is cut out of each corner, diameter is approximately 14 feet. What is the approximate area (in square feet) of the remaining portion of the circle? 80 ft² 50 ft² 40 ft² 25 ft²

A square is cut out of each corner, diameter is approximately 14 feet. What is the approximate area (in square feet) of the remaining portion of the circle?

80 ft² 50 ft² 40 ft² 25 ft²

Transcript text: A square is cut out of each corner, diameter is approximately 14 feet. What is the approximate area (in square feet) of the remaining portion of the circle? 80 ft² 50 ft² 40 ft² 25 ft²

Solution

Solution Steps

Step 1: Calculate the Radius of the Circle

The diameter of the circle is given as \( 14 \) feet. Therefore, the radius \( r \) is calculated as: \[ r = \frac{14}{2} = 7 \text{ feet} \]

Step 2: Calculate the Area of the Circle

Using the formula for the area of a circle \( A = \pi r^2 \), we find: \[ A = \pi (7)^2 = 49\pi \approx 153.9380 \text{ square feet} \]

Step 3: Calculate the Area of One Square

The side length of each square cut out from the corners is \( 10 \) feet. Thus, the area \( A_s \) of one square is: \[ A_s = (10)^2 = 100 \text{ square feet} \]

Step 4: Calculate the Total Area of the Squares Cut Out

Since there are four squares, the total area \( A_{total} \) of the squares cut out is: \[ A_{total} = 4 \times 100 = 400 \text{ square feet} \]

Step 5: Calculate the Remaining Area

The remaining area \( A_{remaining} \) after cutting out the squares from the circle is: \[ A_{remaining} = A - A_{total} = 49\pi - 400 \approx 153.9380 - 400 = -246.0619 \text{ square feet} \]

Final Answer

Since the remaining area is negative, it indicates that the area of the squares cut out exceeds the area of the circle. Therefore, the answer is not valid in the context of the problem.

Thus, the final answer is: \[ \boxed{A \text{ is not valid due to negative area}} \]

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