[tex]\displaystyle V = \pi\int_{0}^1f^2(x)\, dx = \pi \int_{0}^1(1-x)^2\, dx =\\ \\ =-\pi \int_{0}^1(1-x)'\cdot (1-x)^2 dx =-\pi\cdot \dfrac{(1-x)^3}{3}\Big|_{0}^1\\ \\ =-\pi\cdot \dfrac{(1-1)^3}{3}+\pi\cdot \dfrac{(1-0)^3}{3} = \boxed{\dfrac{\pi}{3}}[/tex]
