Step 1 :Set up an integral using the method of cylindrical shells for the volume of the solid. The integral is represented as \(V=\int^{\sqrt{\pi / 2}}(\square) dx\).
Step 2 :Evaluate the integral to find the volume of the solid.
Step 3 :The question does not provide enough information to solve the problem. We need more details about the shaded region and the function to be integrated.
Step 4 :Final Answer: \(\boxed{\text{The question does not provide enough information to solve the problem. We need more details about the shaded region and the function to be integrated.}}\)