Final answer:
To find out how many popcorn bags can be served, calculate the volume of one popcorn bag and divide the total batch volume by this number. In this case, the machine fills approximately 13 full bags.
Step-by-step explanation:
To determine how many bags of popcorn can be served from a single batch, we first need to calculate the volume of a single popcorn bag. The bag is shaped like a rectangular prism, and its volume can be found using the formula:
volume of a rectangular prism = length × width × height
For the popcorn bag, this gives us:
volume of a popcorn bag = 3 in × 2 in × 8.5 in = 51 cubic inches
Next, we divide the volume produced by the popcorn machine by the volume of a single bag to find out how many bags can be filled:
number of bags = 665 cubic inches / 51 cubic inches/bag
Calculating this gives us approximately:
number of bags ≈ 13.04
Given that we can't serve a fraction of a bag, we determine that the popcorn machine can fill 13 full bags of popcorn from a single batch.