Maximum volume of a cone shaped cup (KristaKingMath)

► My Applications of Derivatives course: https://www.kristakingmath.com/applic...

Learn how find the largest possible volume of a cone-shaped up made from a circular piece of paper with radius R, where a sector has been removed and sides CA and CB are joined together. To complete this optimization problem, you'll need to draw a picture of the problem and write down what you know. Then you'll imagine that you'll take a vertical slice of the cone shaped cup so that you can use the pythagorean theorem to relate the radius of the paper to the radius and height of the cone. Solve the pythagorean theorem, the constraint equation, for one of the variables so that you can plug it into the optimization equation, which will be the equation for the volume of the cone. Then simplify the equation for the volume, take the derivative and set it equal to 0 to solve for the height. Plug the height back into the pythagorean theorem to find the radius, then plug both values back into the volume equation to find the volume.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com

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