7. The top of a round table with a circumference of 8pi feet is to be completely covered by 4 square pieces of cloth, each with sides of length 4 feet. If none of the pieces overlap, what is the total area of cloth, in square feet, that will hang over the edge of the table top? (A) 32pi -8 (B) 16pi -32 (C) : 64-8pi (D) 64-16pi (E) 16-4pi

To solve this problem, we need to find the area of the round table and the total area of the 4 square pieces of cloth. Then, we can subtract the area of the table from the total area of the cloth to find the area that will hang over the edge of the table top.<br /><br />Given information:<br />- Circumference of the round table: $8\pi$ feet<br />- Side length of each square piece of cloth: 4 feet<br />- Number of square pieces of cloth: 4<br /><br />Step 1: Find the radius of the round table.<br />Circumference of a circle = $2\pi r$<br />$8\pi = 2\pi r$<br />$r = 4$ feet<br /><br />Step 2: Calculate the area of the round table.<br />Area of a circle = $\pi r^2$<br />Area of the round table = $\pi (4)^2 = 16\pi$ square feet<br /><br />Step 3: Calculate the total area of the 4 square pieces of cloth.<br />Area of each square piece of cloth = $4^2 = 16$ square feet<br />Total area of the 4 square pieces of cloth = $4 \times 16 = 64$ square feet<br /><br />Step 4: Calculate the total area of cloth that will hang over the edge of the table top.<br />Total area of cloth = Total area of the 4 square pieces of cloth - Area of the round table<br />Total area of cloth = $64 - 16\pi$ square feet<br /><br />Therefore, the correct answer is (D) $64-16\pi$.