Solution: In spherical coordinates, $\phi$ is the polar angle measured from the positive $z$-axis. When $\phi$ is constant, the set of points forms a cone with its apex at the origin, opening symmetrically around the $z$-axis. For $\phi = \frac\pi4$, the cone makes a $45^\circ$ angle with the $z$-axis. Thus, the shape is a cone. - Nelissen Grade advocaten