In this project we use triple integrals to learn more about hot air balloons. We model the balloon in two pieces. The top of the balloon is modeled by a half sphere of radius 28 feet. The bottom of the balloon is modeled by a frustum of a cone (think of an ice cream cone with the pointy end cut off). The radius of the large end of the frustum is 28 feet and the radius of the small end of the frustum is 6 feet. A graph of our balloon model and a cross-sectional diagram showing the dimensions are shown in the following figure.Find the average temperature of the air in the balloon after the pilot has activated the burner for 10 seconds.

ZI ZA 50 40 30 28 ft 40 50 50-40-30 30 40 50 X 44 ft 12 ft 50 (a) (b )