Here is an attempt:
With[{r = .6},
Show[ParametricPlot3D[Table[{r Cos[c + t], r Sin[c + t], 2 t},
{c, 0, 2 Pi, Pi/15}],
{t, 0, Pi/4}, PlotStyle -> Directive[Black, Thin]],
Graphics3D[{ResourceFunction["Annulus3D"][{{0, 0, 0},
{0, 0, Pi/2}}, .6],
Table[Line[{{r/2 Cos[Pi/4 + c], r/2 Sin[Pi/4 + c],
Pi/2}, {r*Cos[Pi/4 + c], r*Sin[Pi/4 + c], Pi/2}}],
{c, 0, 2 Pi, Pi/15}]}],
BoxRatios -> {1, 1, 1}]]