Final answer:
To calculate the number of gum balls the machine can hold, we need to find the volumes of the glass sphere and one gum ball and divide them.
Step-by-step explanation:
To calculate the number of gum balls the machine can hold, we need to find the volume of the glass sphere and divide it by the volume of one gum ball. The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius. The radius of the glass sphere is 2 feet, so the volume would be V = (4/3)π(2)³. We also need to convert the radius of one gum ball from inches to feet, which is 1.2/12 = 0.1 feet. The volume of one gum ball would then be V = (4/3)π(0.1)³. Finally, we can calculate the number of gum balls the machine can hold by dividing the volume of the glass sphere by the volume of one gum ball: (4/3)π(2)³ / (4/3)π(0.1)³ = (2)³ / (0.1)³ = 8 / 0.001 = 8,000 gum balls.