Introduction:
The problem states that there is a hollow metal tube with a charge at its center. We need to determine the electric flux through the curved surfaces of the tube.

Understanding Electric Flux:
Electric flux is a measure of the electric field passing through a given area. It is defined as the dot product of the electric field vector and the area vector. Mathematically, it is represented as Φ = E * A * cos(θ), where E is the electric field, A is the area, and θ is the angle between the electric field and area vectors.

Electric Flux through Curved Surfaces:
The electric flux through the curved surfaces of the hollow metal tube can be determined using Gauss's law. According to Gauss's law, the total electric flux passing through a closed surface is equal to the total charge enclosed divided by the permittivity of the medium.

Applying Gauss's Law:
To calculate the flux through the curved surfaces, we need to consider a Gaussian surface that encloses the charge at the center of the tube. The Gaussian surface should be chosen such that it only intersects the curved surfaces of the tube.

Flux Calculation:
1. Choose a Gaussian surface that encloses the charge at the center of the tube and only intersects the curved surfaces.
2. The flux through the curved surfaces can be calculated by subtracting the flux through the plane surfaces from the total flux passing through the Gaussian surface.
3. The flux through the plane surfaces is given as Φ = phi, as mentioned in the problem.
4. The total flux through the Gaussian surface can be calculated by dividing the total charge enclosed by the permittivity of the medium.
5. Once the total flux is calculated, subtract the flux through the plane surfaces to obtain the flux through the curved surfaces.

Conclusion:
To determine the flux through the curved surfaces of a hollow metal tube with a charge at its center, we need to apply Gauss's law. By choosing a Gaussian surface that encloses the charge and only intersects the curved surfaces, we can calculate the total flux passing through the Gaussian surface. Subtracting the flux through the plane surfaces from the total flux will give us the flux through the curved surfaces.