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

$V$ = $32$

cross section height $\frac{8}{8-x}$ = $\frac{4}{h}$ $h$ = $\frac{1}{2}(8-x)$ base $\frac{8}{8-x}$ = $\frac{6}{b}$ $b$ = $\frac{3}{4}(8-x)$ $V$ = $\int_0^{8}\frac{1}{2}[\frac{3}{4}(8-x)][\frac{1}{2}(8-x)]dx$ $V$ = $\int_0^{8}\frac{3}{16}(8-x)^{2}dx$ $V$ = $\int_0^{8}\frac{3}{16}(64-16x+x^{2})dx$ $V$ = $\frac{3}{16}(64x-8x^{2}+\frac{1}{3}x^{3})|_0^8$ $V$ = $32$