Answer: the largest possible circular table top that can be cut out of the square piece of wood has an area of approximately 48.94 square feet.
Step-by-step explanation:
To find the area of the largest possible circular table top that can be cut out of the square wood, we can use the formula for the area of a circle:A = πr^2where A is the area of the circle, π is the constant 3.14, and r is the radius of the circle.Knowing that the length of the side of the square piece of wood is 4.5, we can calculate the radius of the circle as follows:r = sqrt(a/π)where r is the radius of the circle and a is the area of the circle.Substituting the desired area for a, we get:r = 4.5/sqrt(π) ≈ 2.9Therefore, the radius of the largest possible circular table top that can be cut out of the wood is approximately 2.9, and the area of this circle is:A = π*r^2 ≈ 48.94Therefore, the largest possible circular table top that can be cut out of the square piece of wood has an area of approximately 48.94 square feet.
