As part of the International Baccalaureate Diploma program(me) (IB for short, I BS for laughs) during my high school years, I had to write an Extended Essay. As Mathematics was one of my favorite subjects, I decided to write mine on a topic mathematical in nature. I had learned about solids of revolution in Calculus sophomore year, and I had just finished IB Higher Math, in which the topic of linear transformation was taught. In a rare moment of intellectual transcendence, I decided to combine the two topics and figure out how solids of revolution worked about axes that were neither parallel to the X nor parallel to the Y.
The ideas, text, and figures are all original (i.e., I did not pull the method out of a textbook). I provided the references at the end for my bibliography because I did not know what else to put. At the time, I thought that my synthesis of the two topics was revolutionary. Alas, time proves youth a fool. Nevertheless, it was one of my more enjoyable and well-written pieces.
Download The Application of Linear Transformations in Finding the Volumes of Solids of Revolutions [sic] About Slant Axes Using the Disc/Washer Method (326 KB).