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? Use 3.14 for pi
What is the total volume of the balloon? Use 3.14 for pi and round your answer to the nearest tenth.
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the cone and h is its height.
In this case, the radius of the cone is 12 feet and the height is 60 feet. Substituting these values into the formula, we get V_cone = (1/3)π(12^2)(60) = 3.14(144)(60) = 6782.4 cubic feet.
The volume of a hemisphere can be calculated using the formula V = (2/3)πr^3, where r is the radius of the hemisphere.
In this case, the radius of the hemisphere is also 12 feet. Substituting this value into the formula, we get V_hemisphere = (2/3)π(12^3) = 3.14(2)(1728) = 10823.52 cubic feet.
To find the total volume of the balloon, we add the volume of the cone and the volume of the hemisphere: V_total = V_cone + V_hemisphere = 6782.4 + 10823.52 = 17605.92 cubic feet.
Therefore, approximately 17605.92 cubic feet of helium will be needed to fill the balloon.