A gigantic balloon used for a parade is shaped like an ice cream cone the radius of the cone and the hemisphere is 12 feet the height of the cone is 60 feet if the balloon is filled with helium how much helium will be needed to fill the balloon part a what is the volume of the hemisphere part B what is the volume of the cone part C what is the total volume of the balloon
To solve this problem, we will calculate the volume of the hemisphere and the cone separately, and then add them together to find the total volume of the balloon.
Part A: Volume of the Hemisphere
The formula for the volume of a hemisphere is V = (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:
V = (2/3) * π * (12)^3
= (2/3) * π * 1728
≈ 3617.6 cubic feet
Therefore, the volume of the hemisphere is approximately 3617.6 cubic feet.
Part B: Volume of the Cone
The formula for the volume of a cone is V = (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 of the cone is 60 feet, we can substitute these values into the formula:
V = (1/3) * π * (12)^2 * 60
= (1/3) * π * 144 * 60
= (1/3) * π * 8640
≈ 9047.8 cubic feet
Therefore, the volume of the cone is approximately 9047.8 cubic feet.
Part C: Total Volume of the Balloon
To find the total volume of the balloon, we need to add the volume of the hemisphere and the volume of the cone:
Total volume = volume of hemisphere + volume of cone
= 3617.6 + 9047.8
≈ 12665.4 cubic feet
Therefore, the total volume of helium needed to fill the balloon is approximately 12665.4 cubic feet.