Step 1 :Find the volume of the solid generated by revolving the region bounded by the graph of \(y=x^2\), the vertical line \(x=3\), and the horizontal line \(y=4\) about the horizontal line \(y=4\) using the disk method. The radius of each disk is \(4-x^2\) and the area of each disk is \(\pi(4-x^2)^2\). Integrate this area from \(x=0\) to \(x=3\).
Step 2 :Evaluate the integral to find the volume: \(\boxed{\frac{123\pi}{5}}\)