Answer
$\dfrac{\pi}{6}$
Work Step by Step
The point of intersection can be computed as:
$a \sqrt {x-ax^2}=0 \\x -ax^2=0 \\ x=0; \dfrac{1}{a}$
The volume of a solid by using the disk method can be calculated as:
$Volume, V=\pi \int_{m}^{n} R^2 \ dx \\= \pi \int_{0}^{1/a} (a \sqrt {x-ax^2})^2 \ dx \\=\pi \int_{0}^{1/a} a^2 x -a^3 x^2 \ dx\\=\pi [\dfrac{a^2x^2}{2}-\dfrac{a^3x^3}{3}]_{0}^{1/a} \\=\pi [\dfrac{1}{2} -\dfrac{1}{3}] \\=\dfrac{\pi}{6}$
