Original: The standard kilogram is in the shape of a circularcylinder with its height equal to its diameter. Show that, for acircular cylinder of fixed volume, this equality gives the smallestsurface area, thus minimizing the effects of surface contaminationand wear.
Modified: #18 is a classic problem which usually goes by the title:design the soda can that has the smallest surface area for a givenvolume. You'll need to use some info on platinum from the back ofthe book (iridium is small taters, here). This is a big project inmiddle school so there should be plenty of graphing solutions forthis problem on the internet. We'll solve it with calculus in classand the just-started-calcs will see some fun math. Read abouthydrogen diffusion into metals to see that even solid platinumgains weight in the real world. For that reason, the InternationalStandard kilogram remains forever entombed inside several highlyevacuated bell jars. Relax, its early.
Original: The standard kilogram is in the shape of a circularcylinder with its height equal to its diameter. Show that, for acircular cylinder of fixed volume, this equality gives the smallestsurface area, thus minimizing the effects of surface contaminationand wear.
Modified: #18 is a classic problem which usually goes by the title:design the soda can that has the smallest surface area for a givenvolume. You'll need to use some info on platinum from the back ofthe book (iridium is small taters, here). This is a big project inmiddle school so there should be plenty of graphing solutions forthis problem on the internet. We'll solve it with calculus in classand the just-started-calcs will see some fun math. Read abouthydrogen diffusion into metals to see that even solid platinumgains weight in the real world. For that reason, the InternationalStandard kilogram remains forever entombed inside several highlyevacuated bell jars. Relax, its early.
