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
3,617.3 ft3
3,617.3 ft3
7,234.6 ft3
7,234.6 ft3
5,425.9 ft3
5,425.9 ft3
21,703.7 ft3
21,703.7 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
36,172.8 ft3
36,172.8 ft3
27,129.6 ft3
27,129.6 ft3
753.6 ft3
753.6 ft3
9,043.2 ft3
9,043.2 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
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Part A: The volume of a hemisphere is given by the formula V = (2/3)πr^3, where r is the radius of the hemisphere. In this case, the radius is 12 feet. Plugging this value into the formula, we get:
V = (2/3)π(12^3)
V = (2/3)(3.14)(1728)
V ≈ 3617.3 ft^3
Therefore, the volume of the hemisphere is approximately 3617.3 ft^3.
Part B: The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone. In this case, the radius and height are both 12 feet. Plugging these values into the formula, we get:
V = (1/3)π(12^2)(60)
V = (1/3)(3.14)(144)(60)
V ≈ 27,129.6 ft^3
Therefore, the volume of the cone is approximately 27,129.6 ft^3.
Part C: The total volume of the balloon is the sum of the volume of the hemisphere and the volume of the cone. Adding the volumes calculated in Part A and Part B, we get:
Total volume = 3617.3 ft^3 + 27,129.6 ft^3
Total volume ≈ 30,746.9 ft^3
Therefore, the total volume of the balloon is approximately 30,746.9 ft^3.