Answer
$\dfrac{4 \pi}{3}$
Work Step by Step
Since, the vertical slices solid are circular discs , so we will use the disk method to compute the volume of revolution of the curve.
The volume of revolution of the curve can be expressed as: $V=\pi \int_p^q [f(x)]^2 dx\\=\pi \int_0^1 (2-2x)^2 \ dx \\=4 \pi \int_0^1 (1-x)^2 \ dx \\=4 \pi \int_0^1 1-2x+x^2 dx \\=4 \pi [x-x^2 +\dfrac{x^3}{3}]_0^1 \\=\dfrac{4 \pi}{3}$
