Solids of Revolution

Core Sentence / 核心句

A solid of revolution is measured by rotating a representative slice and accumulating the resulting disk or washer areas.

$$A_{\text{disk}}=\pi R^2,A_{\text{washer}}=\pi (R^2-r^2).$$

Key Rule / 关键规则

Radius is distance to the axis of rotation. For a shifted axis, subtract coordinates; do not automatically use the raw function value.

Connected Notes / 连接

• 微积分BC第12次正课-旋转体弧长参数向量与极坐标
• Cross-Sectional Volume
• Area Between Curves
• Integrals