## Calculus (3rd Edition)

$\dfrac{625 \pi }{6}$
We calculate the volume using the disk method: $V=\pi \int_{m}^{n} (R^2) \ dy \\=\pi \int_0^5 [y(5-y)] \ dy \\=\pi \int_0^5 y^2(5-y)^2 \ dy \\=\pi \int_0^5 y^2 (25-10y+y^2) \ dy \\= \pi \int_0^5 (25y^2-10y^3+y^4) \ dy _0^2 \\=\pi [\dfrac{25y^3}{3}-\dfrac{10y^4}{4}+\dfrac{y^5}{5}]_0^5 \\=\dfrac{625 \pi }{6}$