To find the volume of revolution, we use the formula:

\(V = \pi \int_{a}^{b} y^2 \, dx\)

Given \(y = \sqrt{x^4 + 4x + 4}\), we have:

\(y^2 = x^4 + 4x + 4\)

Integrate \(y^2\) from \(x = -1\) to \(x = 0\):

\(\int (x^4 + 4x + 4) \, dx = \left[ \frac{x^5}{5} + 2x^2 + 4x \right]\)

Apply the limits:

\(\pi \left[ \left( \frac{0^5}{5} + 2(0)^2 + 4(0) \right) - \left( \frac{(-1)^5}{5} + 2(-1)^2 + 4(-1) \right) \right]\)

\(= \pi \left[ 0 - \left( -\frac{1}{5} + 2 - 4 \right) \right]\)

\(= \pi \left[ 0 - \left( -\frac{1}{5} - 2 \right) \right]\)

\(= \pi \left[ \frac{1}{5} + 2 \right]\)

\(= \pi \left[ \frac{11}{5} \right]\)

Thus, the volume of revolution is \(\frac{11\pi}{5}\).