Students in Cathy Douglas’s and Lisa Kramer’s Calculus Accelerated classes are in the thick of a unit on the disk method and volumes by rotation.
In today’s “opener” (an exercise used to get the math brain engaged), students were asked to find the volume of a Hostess cupcake by (a) a traditional formula for a truncated cone and (b) “by finding a function that can be rotated about an axis to create the shape, then using calculus to find the volume.” (!) The class compared the two results to see if the volumes were identical.
Students were also asked to determine whether their findings were consistent with the volume listed on the cupcake package. Their results showed about 10 additional cubic centimeters over the package’s listed 45 grams (the gram was originally defined as the mass of one cubic centimeter of water at its maximum density at 4 degrees Celsius). “The creamy spherical filling seemed to be less dense,” says Cathy. “One of my students estimated the cubic centimeters of the creamy filling and found that it accounted for the difference in our volumes and the package’s unit weight.”
Needless to say, the subject matter was consumed at the end of the class…