Cross-Sectional Volume

Core Sentence / 核心句

A volume with known cross sections accumulates cross-sectional area times infinitesimal thickness.

V = \int_{a}^{b} A (x) d x or V = \int_{c}^{d} A (y) d y .

Draw a perpendicular slice -> find its base length $L$ from the region -> express the cross-section area $A (L)$ -> integrate across the base.

先确认题目给的是 radius、diameter、leg 还是 base。截面垂直于 $x$ -axis 通常使用 $d x$ ；垂直于 $y$ -axis 通常使用 $d y$ 。