Question

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. Show your work.



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

5,425.9 ft3
5,425.9 ft3

21,703.7 ft3
21,703.7 ft3

7,234.6 ft3
7,234.6 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

36,172.8 ft3
36,172.8 ft3

27,129.6 ft3
27,129.6 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

Answer 1

Given: radius r = 12 ft, cone height h = 60 ft, use π = 3.14.

Part A — Hemisphere
Volume of a hemisphere = (1/2)*(4/3)πr^3 = (2/3)πr^3.
r^3 = 12^3 = 1728, so volume = (2/3)*3.14*1728 = 1152 * 3.14 = 3617.28 ft^3.
Rounded to one decimal: 3617.3 ft^3.

Answer: 3,617.3 ft^3

Part B — Cone
Volume of a cone = (1/3)πr^2h.
r^2 = 144, so volume = (1/3)*3.14*144*60 = 2880 * 3.14 = 9043.2 ft^3.
Rounded to one decimal: 9043.2 ft^3.

Answer: 9,043.2 ft^3

Part C — Total volume
Total = hemisphere + cone = 3617.28 + 9043.2 = 12,660.48 ft^3.
Rounded to one decimal: 12,660.5 ft^3.

Total volume: 12,660.5 ft^3