Chapter 6 - Applications of the Integral - 6.2 Setting Up Integrals: Volume, Density, Average Value - Exercises - Page 297: 15

$V$ = $\frac{\pi}{3}$

radius at lower half is $y+1$ radius at upper half is $1-y$ $V$ = $\frac{\pi}{2}\int_{-1}^{0}(y+1)^{2}dy$ + $\frac{\pi}{2}\int_{0}^{1}(1-y)^{2}dy$ $V$ = $\frac{\pi}{2}(\frac{1}{3}+\frac{1}{3})$ $V$ = $\frac{\pi}{3}$