Final answer:
To find the amount of wood wasted when cutting the largest possible circular tabletop from a square with a side length of 2 feet, calculate the area of the square and subtract the area of the circle. The amount of wood wasted is 0.86 square feet.
Step-by-step explanation:
To find the amount of wood wasted when cutting the largest possible circular tabletop from a square with a side length of 2 feet, we need to calculate the area of the square and subtract the area of the circle.
The area of the square is found by multiplying its side length by itself: 2 feet x 2 feet = 4 square feet.
The largest possible circular tabletop that can be cut from this square will have a diameter equal to the side length of the square, which is 2 feet. The radius of the circular tabletop will be half of the diameter, so the radius is 1 foot.
Using the formula for the area of a circle, A = πr², we can calculate the area of the circular tabletop: A = 3.14 x (1 foot)² = 3.14 square feet.
To find the amount of wood wasted, subtract the area of the circular tabletop from the area of the square:
4 square feet - 3.14 square feet = 0.86 square feet.
Therefore, the correct answer is D. 0.86 square feet.