Final answer:
The Willis Tower has a footprint area of 50,625 square feet and a total volume of 25,312,500 cubic feet for all nine tubes. The average temperature difference per tube is 10°C. Sound takes approximately 0.444 seconds to travel from the top to the bottom of one tube.
Step-by-step explanation:
Willis Tower Footprint and Volume Calculations
To find the total footprint area of the Willis Tower, we multiply the length by the width of the building's square base. Since the building has a 225-foot by 225-foot square base, the area is 225 ft × 225 ft, which equals 50,625 square feet.
To calculate the total volume of the tower if each of the nine tubes extends to a height of 500 feet, we first calculate the volume of one tube by multiplying the cross-sectional area of one tube (which is one-ninth of the total footprint area) by the height of the tube. The area of one tube is 50,625 square feet ÷ 9 = 5,625 square feet. Therefore, the volume of one tube is 5,625 square feet × 500 feet = 2,812,500 cubic feet. The total volume of all nine tubes is 2,812,500 cubic feet × 9 = 25,312,500 cubic feet.
The average temperature difference per tube if the top is 10°C and the bottom is 20°C is simply the difference in temperature, which is 20°C - 10°C = 10°C. Because we are given the temperatures at two points, the 'average' temperature difference is simply the difference itself.
To calculate how long it takes for sound to travel from the top to the bottom of one tube, we use the speed of sound provided (343 m/s) and the height of the tube in meters. First, we convert the height into meters: 500 feet × 0.3048 m/ft = 152.4 meters. Then, time is calculated by dividing the height by the speed of sound: 152.4 m ÷ 343 m/s ≠ 0.444 seconds.