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
5,425.9 ft3
5,425.9 ft3
21,703.7 ft3
21,703.7 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
27,129.6 ft3
27,129.6 ft3
753.6 ft3
753.6 ft3
36,172.8 ft3
36,172.8 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
Part A:
The formula for the volume of a hemisphere is (2/3)πr^3.
Given that the radius of the hemisphere is 12 feet, we can substitute this value into the formula:
Volume = (2/3)π(12^3)
Volume = (2/3)π(1728)
Volume ≈ 11419.2 ft^3
The volume of the hemisphere is approximately 11419.2 ft^3.
Part B:
The formula for the volume of a cone is (1/3)πr^2h.
Given that the radius of the cone is 12 feet and the height of the cone is 60 feet, we can substitute these values into the formula:
Volume = (1/3)π(12^2)(60)
Volume = (1/3)π(144)(60)
Volume ≈ 9043.2 ft^3
The volume of the cone is approximately 9043.2 ft^3.
Part C:
To find the total volume of the balloon, we need to add the volumes of the hemisphere and the cone:
Total volume = Volume of hemisphere + Volume of cone
Total volume ≈ 11419.2 + 9043.2
Total volume ≈ 20462.4 ft^3
The total volume of the balloon is approximately 20462.4 ft^3.