Chapter 6 - Section 6.1 - Volumes Using Cross-Sections - Exercises - Page 357: 61

$$3308 cm^3$$

We need to integrate the integral to compute the volume. We have: $$Volume= \pi \times \int_{-16}^{-7} (256-y^2) \space dy \\= [256 y-\dfrac{y^3}{3}]_{-16}^{-7} \times \pi \\= [256 \space (7) y-\dfrac{(343)}{3}+256(16)-(4096/3)] \times \pi =1053 \pi\approx 3308 cm^3$$