Final answer:
To determine how much of the tablecloth will be showing when the table is set for six people, subtract the area of the dinner plates from the area of the table.
Step-by-step explanation:
To determine how much of the tablecloth will be showing when the table is set for six people, we need to find the total area of the dinner plates and subtract it from the area of the dinner table. The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius. Since the diameter of the table is 8 feet, the radius is 4 feet. Therefore, the area of the table is A = π(4)^2 = 16π square feet.
Each dinner plate has a diameter of 1 foot, so the radius is 0.5 feet. The area of one dinner plate is A = π(0.5)^2 = 0.25π square feet. Since there are 6 people, there will be 6 dinner plates on the table. Therefore, the total area of the dinner plates is 6 * 0.25π = 1.5π square feet.