Cavalieri's Principle

Theorem

• Suppose $R$ is a Domain in ${\mathbb{R}}^3$ contained between $z=a$, $z=b$
• Let $A(t)=Area(R\cap \{z=t\})$ be the area of the slice of $R$ at height $t$
• $Vol(R)={\int }_a^{b}A(t)dt$