Riley, have you ever noticed aluminum cans? {{CMD_7}} So very recyclable! {{CMD_8}} I know! But I've also noticed that there are some that are short and fat, and others that are tall and skinny, and yet they can still have the same volume! {{CMD_9}} So very observant! {{CMD_10}} This got me wondering, if we want to make a can with volume {{MATH_11}}, what shape of can uses the least aluminum? {{CMD_12}} Ah! This sounds like a job for calculus! The volume of a cylindrical can is given by {{MATH_13}} where {{MATH_14}} is the radius of the cylinder and {{MATH_15}} is the height of the cylinder. Also the surface area is given by {{ENV_16}} Somehow we want to minimize the surface area, because that's the amount of aluminum used, but we also want to keep the volume constant. {{CMD_17}} Whoa, we have way too many letters here. {{CMD_18}} Yeah, somehow we need only one variable. Yikes. Too many letters. {{CMD_19}}