Answer
$\dfrac{ \pi c^2}{2}$
Work Step by Step
The shell method to compute the volume of a region: The volume of a solid obtained by rotating the region under $y=f(x)$ over an interval $[m,n]$ about the y-axis is given by:
$V=2 \pi \int_{m}^{n} (Radius) \times (height \ of \ the \ shell) \ dy=2 \pi \int_{m}^{n} (y) \times f(y) \ dy$
Now, $V=2\pi \int_{0}^{\sqrt c} x (c-x^2) \ dx\\= 2 \pi \int_0^{\sqrt c} (cx-x^3) \ dx \\= 2 \pi [\dfrac{cx^2}{2}+\dfrac{x^4}{4}]_0^{\sqrt c} \\=\dfrac{ \pi c^2}{2}$
