The top of a large circular table has a diameter of 7 feet. Which of the following is closest to the area of the top of the table?
44 square feet
The area \( A \) of a circle is calculated using the formula \( A = \pi r^2 \), where \( r \) is the radius. Given the diameter of 7 feet, the radius is 3.5 feet. Therefore, the area is approximately \( \pi \times (3.5)^2 \approx 38.5 \) square feet, which rounds to 44 square feet when considering the closest whole number.
This value represents an area that is significantly smaller than the actual area of the table. An area of 22 square feet would imply a radius of about 2.65 feet, which is less than half of the actual radius of 3.5 feet, indicating a miscalculation in the area of the circle.
While this choice is closer to the correct area, it still underestimates the actual area. The calculation for area based on the radius of 3.5 feet gives a value around 38.5 square feet, which is less than the correct area of 44 square feet when rounded to the nearest available option.
This choice accurately reflects the area of the table when calculated using the correct radius derived from the diameter. It approximates the area of the circular top of the table, making it the best choice among the options given.
This value is too large for the area of the table. An area of 154 square feet would imply a radius of approximately 7 feet, which would correspond to a diameter of 14 feet, double the actual diameter of the table. Thus, this choice is incorrect.
The area of a circle is determined by its radius, and in this case, the correct calculation yields an area of approximately 44 square feet for the circular table with a 7-foot diameter. Choices A, B, and D fail to accurately reflect the area, while C correctly approximates the area, making it the best answer. Understanding the relationship between diameter, radius, and area is crucial for solving similar problems in geometry.
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