Friends School of Minnesota 7th graders embarked on another geometry challenge this week involving popcorn! Everyone knows that movie theater popcorn often comes in buckets, similar in shape to a cylinder. Not everyone knows that the volume of popcorn received varies dramatically with the height of the bucket, even when the lateral surface area remains unchanged. The design challenge for students was to compare popcorn bucket volumes using a lateral surface made from one sheet of 8 1/2″ x 11″ paper. This was their only constraint.
Many kids were surprised that the shorter the bucket (and therefore greater the base), the greater the volume of popcorn! As the circumference grew and the radius becomes gigantic, the popcorn got so shallow that the reality of filling and eating from the bowl became quite difficult! So “the best bowl” vs “the biggest bowl” became the real question. Please look at the photos to get an idea of the prototypes the students built, and the popcorn they enjoyed.
— Kris Bennett, FSM Math Teacher