Untangling Volumes by Michelle

Untangling Volumes by Michelle - July 2026 Scholarship Essay

The last unit of the AP Calculus AB curriculum – volumes. Just the word used to conjure images of endless practice, a blur of instructional videos, and far too many sleepless nights. It was, without a doubt, the greatest challenge of my calculus journey. Up until then, calculus class had been a relatively smooth sail, until volumes came along.

I still vividly remember the substitute teacher, a kind but unfamiliar face, distributing Play-Doh for us to sculpt cross-sections. I fumbled with the clay, my square shapes collapsing into shapeless blobs. At the time, I brushed it off, grateful for the respite from the usual intensity of AP Calculus. The next class, however, shattered that illusion of a temporary diversion. Our regular teacher held up the very cross-sectional squares that were supposed to be our masterpieces. Mine, of course, was absent. "This can't be real," I thought, staring blankly at the whiteboard, the concept of volumes an indecipherable puzzle.

The homework assigned that day only deepened my discouragement. Despite my initial motivation to conquer it, the clock ticked by with no real understanding gained. College Board videos, usually my trusty guides, offered no clarity. I decided to leave it, convinced that sleep would somehow untangle the knot in my brain. The next day brought no insights. I scoured my textbook, watched countless online tutorials, and even resorted to AI explanations – all to no avail. Eventually, I scribbled down whatever I could, knowing it was likely incorrect, and submitted my first-ever incomprehensible calculus assignment.

Yet, a stubborn refusal to be defeated gnawed at me. During consultation hours, I sought out my teacher, determined to unravel the mystery of volumes. Even as the explanation washed over me with limited comprehension, I remained steadfast. That night, with all other assignments complete, I returned to battle this beast. I lost count of the College Board, Khan Academy, and YouTube videos I devoured. And then, amidst the flurry of numbers and diagrams, a sense of peace settled over me.
What I had been missing was the connection – the underlying pattern that linked different problems and allowed for the consistent application of learned formulas. I discovered how to effectively categorize problems, identifying the specific method required for each. The puzzle pieces finally clicked into place.

Volumes had been my roughest patch of water, but I sailed through it. More than that, it taught me to stop searching for one formula to memorize and start asking what kind of problem I was looking at. That shift of learning to categorize before I calculate has changed how I approach every hard problem since, in calculus and outside it.