Chapter 6 - Applications of the Integral - 6.2 Setting Up Integrals: Volume, Density, Average Value - Exercises - Page 296: 7

$V$ = $\frac{1}{6}abc$

line c to a is given equation $\frac{z}{c}+\frac{x}{a}$ = $1$ $z$ = $c(1-\frac{x}{a})$ line b to a is given equation $\frac{y}{b}+\frac{x}{a}$ = $1$ $y$ = $b(1-\frac{x}{a})$ $V$ = $\int_0^{a}\frac{1}{2}bc(1-\frac{x}{a})^{2}dx$ $V$ = $-\frac{1}{6}abc(1-\frac{x}{a})^{3}|_0^a$ $V$ = $\frac{1}{6}abc$