Answer:
The total volume of helium needed to fill the balloon is approximately 16,277.8 ft^3.
Explanation:
To calculate the volume of the balloon, we need to find the volumes of the hemisphere and the cone separately, and then add them together.
A) Volume of the hemisphere:
The formula for the volume of a hemisphere is (2/3) * π * r^3, where r is the radius.
Given that the radius of the hemisphere is 12 feet, we can substitute this value into the formula:
Volume = (2/3) * 3.14 * (12)^3 ≈ 7,234.6 ft^3
B) Volume of the cone:
The formula for the volume of a cone is (1/3) * π * r^2 * h, where r is the radius and h is the height.
Given that the radius of the cone is also 12 feet and the height is 60 feet, we can substitute these values into the formula:
Volume = (1/3) * 3.14 * (12)^2 * 60 ≈ 9,043.2 ft^3
C) Total volume of the balloon:
To find the total volume, we add the volume of the hemisphere and the volume of the cone:
Total volume = Volume of hemisphere + Volume of cone
Total volume = 7,234.6 ft^3 + 9,043.2 ft^3 ≈ 16,277.8 ft^3
Summary:
A) The volume of the hemisphere is approximately 7,234.6 ft^3.
B) The volume of the cone is approximately 9,043.2 ft^3.
C) The total volume of the balloon is approximately 16,277.8 ft^3.