The curve intersects \(y = 1\) at \((3, 1)\).

Volume = \(\pi \int (x-2) \,[dx]\)

\(\left[ \pi \left( \frac{1}{2} x^2 - 2x \right) \right] \text{ or } \left[ \pi \left( \frac{1}{2} (x-2)^2 \right) \right]\)

= \(\left[ \pi \left( \frac{5^2}{2} - 2 \times 5 \right) - \left( \text{their } 3^2/2 - 2 \times \text{their } 3 \right) \right]\)

= \(\left[ \pi \left( \frac{5}{2} + \frac{3}{2} \right) \right] \text{ as a minimum requirement for their values}\)

Volume of cylinder = \(\pi \times 1^2 \times (5 - \text{their } 3) = [2\pi]\)

\([Volume of solid = 4\pi - 2\pi =] 2\pi \text{ or } 6.28\)