Chapter 6: Applications of Definite Integrals - Section 6.1 - Volumes Using Cross-Sections - Exercises 6.1 - Page 323: 57

$3308 \space cm^3$

We integrate the integral to calculate the volume as follows: $V= \pi \times \int_{-16}^{-7} (256-y^2) dy$ Now, $V= \pi \times [256 y-\dfrac{y^3}{3}]_{-16}^{-7}$ or, $Volume= \pi \times [256 (7) y-\dfrac{(343)}{3}+256(16)-(4096/3)]=1053 \pi =3308 \space cm^3$