Equations like \(A=B\cdot H\), \(A=\pi r^2\), or even \(V=\pi r^2\cdot h\) are familiar to everyone, and might even be a little traumatic as they bring you back to your high school math days.
Whether you liked learning about area and volume as a student, one can't deny the influence that they have in mathematics. These ideas are havily emphasized throughout geometry units, and even influence
topics tuaght in higher level math classes. Students are expected to identify the correct formulas for both area and volume for each shape and know how to find the answer using those formulas. While
students are very comfortable with the ideas of area and volume by the time they graduate high school, oftentimes students aren't taught the history behind these concepts, where these formulas came from
and some useful applications for area and volume. Throughout this paper, the reader will understand some of the history of area and volume in additioin to seeing how formulas can be derived and proven through calculus along with calculus based applications.