## University Calculus: Early Transcendentals (3rd Edition)

$$32\pi$$
The paraboloid will intersect the $xy$-plane when $9-x^2-y^2=0 \implies x^2+y^2=9$ Our aim is to integrate the integral as follows: $$volume=(4) \times \int^{\pi/2}_0 \int^3_1 \int^{9-r^2}_0 dz \space r dr \space d\theta \\=(4) \times \int^{\pi/2}_0 \int^3_1 (9r-r^3)dr \space d\theta \\=(4) \times \int^{\pi/2}_0 [\dfrac{9}{2} \times r^2-\dfrac{r^4}{4}]^{3}_1 d\theta \\=(4) \int^{\pi/2}_0 (\dfrac{81}{4}-\dfrac{17}{4})d\theta\\=32\pi$$