Chapter 6 - Applications of the Integral - 6.2 Setting Up Integrals: Volume, Density, Average Value - Exercises - Page 296: 2

a) $A$ = $\pi(4-\frac{2}{5}y)^{2}$ b) $V$ = $\frac{160\pi}{3}$

a) r = radius y = height $\frac{10}{4}$ = $\frac{10-y}{r}$ $r$ = $\frac{2}{5}(10-y)$ $A$ = $\pi{r}^{2}$ $A$ = $\pi[{\frac{2}{5}(10-y)}]^{2}$ $A$ = $\pi(4-\frac{2}{5}y)^{2}$ b) $V$ = $\int_0^{10}\pi(4-\frac{2}{5}y)^{2}dy$ $V$ = $-\frac{5\pi}{6}(4-\frac{2}{5}y)^{3}|_0^{10}$ $V$ = $\frac{160\pi}{3}$