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.
Part A
What is the volume of he hemisphere? Use 3.14 for pi and round your answer to the nearest tenth (one decimal place).
(1 point)
Responses
7,234.6 ft3
7,234.6 ft3
21,703.7 ft3
21,703.7 ft3
5,425.9 ft3
5,425.9 ft3
3,617.3 ft3
3,617.3 ft3
Question 2
Part B
What is the volume of the cone? Use 3.14 for pi and round your answer to the nearest tenth.
(1 point)
Responses
753.6 ft3
753.6 ft3
9,043.2 ft3
9,043.2 ft3
27,129.6 ft3
27,129.6 ft3
36,172.8 ft3
36,172.8 ft3
Question 3
Part C
What is the total volume of the balloon? Use 3.14 for pi and round your answer to the nearest tenth.
(1 point)
Total volume:
ft3
Part A:
The volume of a hemisphere is given by the formula V = (2/3)πr³, where r is the radius of the hemisphere.
In this case, the radius of the hemisphere is 12 feet.
V = (2/3)(3.14)(12³) = 2(3.14)(1728) ≈ 10853.8 ft³
So, the volume of the hemisphere is approximately 10853.8 ft³.
Answer: 10,853.8 ft³ (rounded to the nearest tenth)
Part B:
The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius of the cone and h is the height of the cone.
In this case, the radius of the cone is also 12 feet and the height of the cone is 60 feet.
V = (1/3)(3.14)(12²)(60) = (1/3)(3.14)(144)(60) = (1/3)(3.14)(8640) = (3.14)(2880) ≈ 9043.2 ft³
So, the volume of the cone is approximately 9043.2 ft³.
Answer: 9,043.2 ft³ (rounded to the nearest tenth)
Part C:
The total volume of the balloon is the sum of the volumes of the hemisphere and the cone.
Total volume = 10853.8 ft³ + 9043.2 ft³ = 19897 ft³
Answer: 19,897 ft³