The volume \(V\) of the solid of revolution is given by the formula:

\(V = \pi \int_0^1 y^2 \, dx\)

Substitute \(y = \frac{9}{2-x}\) into the formula:

\(V = \pi \int_0^1 \left(\frac{9}{2-x}\right)^2 \, dx\)

\(V = \pi \int_0^1 \frac{81}{(2-x)^2} \, dx\)

Integrate \(\frac{81}{(2-x)^2}\):

\(\int \frac{81}{(2-x)^2} \, dx = -81 \left(2-x\right)^{-1} \times (-1)\)

\(= 81 \left(2-x\right)^{-1}\)

Evaluate from 0 to 1:

\(V = \pi \left[ 81 \left(2-1\right)^{-1} - 81 \left(2-0\right)^{-1} \right]\)

\(= \pi \left[ 81 \times 1 - 81 \times \frac{1}{2} \right]\)

\(= \pi \left[ 81 - 40.5 \right]\)

\(= \pi \times 40.5\)

\(= \frac{81\pi}{2}\)