Final answer:
The volume of the balloon can be calculated by finding the volume of the hemisphere and the cone separately and then adding them together. The time to fill the balloon can be calculated by dividing the total volume by the rate of filling.
Step-by-step explanation:
To find the volume of the balloon, we need to calculate the volume of the hemisphere and the volume of the cone separately, and then add them together.
Volume of hemisphere = (2/3) * pi * r^3, where r is the radius. In this case, r = 12 feet, so the volume of the hemisphere is approximately 7243.7 cubic feet (rounded to the nearest tenth of a cubic foot).
The volume of cone = (1/3) * pi * r^2 * h, where r is the radius and h is the height. In this case, r = 12 feet and h = 60 feet, so the volume of the cone is approximately 9053.3 cubic feet (rounded to the nearest tenth of a cubic foot).
Total volume of the balloon = Volume of hemisphere + Volume of cone = 7243.7 cubic feet + 9053.3 cubic feet = 16297 cubic feet (rounded to the nearest tenth of a cubic foot).
To calculate the time to fill the balloon, we need to divide the total volume by the rate of filling. Given that the rate is 70 cubic feet per minute, the time to fill the balloon is approximately 232.8 minutes (rounded to the nearest minute).