Final answer:
To compare the areas, the 8 inch square has an area of 64 square inches, and the 8 inch round circle, which fits inside the square, has an area of approximately 50.27 square inches, or about three-quarters of the square's area.
Step-by-step explanation:
To compare the areas of an 8 inch square and an 8 inch round circle, we start by calculating the area of each. For the square with a side length (a) of 8 inches, the area (A) is given as A = a² = 8² = 64 square inches. However, for the circle to fit within this square, the diameter of the circle is also 8 inches, making the radius (r) half of that, which is 4 inches. The area of a circle is calculated using the formula A = πr².
Plugging in our radius value, we get A = π × (4²) = π × 16, which is approximately 50.27 square inches (using 3.14 as an approximation for π). The square has the larger area compared to the circle. The circle's area is smaller than that of the square because, while it fits within the square, there are corners of the square not covered by the circle.
The area of the circle is roughly three-quarters of the area of the square. More precisely, the area of the square is 64 square inches, while the area of the circle is approximately 50.27 square inches.