A simple alternative is to use Plot3D with both RegionFunction and Filling.

Plot3D[y, {x, 0, 1}, {y, 0, 1},
 RegionFunction ->
  Function[{x, y, z},
   x^2 + y^2 <= 1 && x >= 0 && y >= 0 && z >= 0],
 Filling -> 0,
 FillingStyle -> Opacity[.75],
 PlotStyle -> Opacity[.5],
 AxesLabel -> (Style[#, 14, Bold] & /@ {x, y, z}),
 BoxRatios -> {1, 1, 1},
 ViewPoint -> {3, -1.5, 0.75}]

A simple alternative is to use Plot3D with both RegionFunction and Filling.

Plot3D[y, {x, 0, 1}, {y, 0, 1},
 RegionFunction ->
  Function[{x, y, z},
   x^2 + y^2 <= 1 && x >= 0 && y >= 0 && z >= 0],
 Filling -> 0,
 FillingStyle -> Opacity[.75],
 PlotStyle -> Opacity[.5],
 AxesLabel -> (Style[#, 14, Bold] & /@ {x, y, z}),
 BoxRatios -> {1, 1, 1},
 ViewPoint -> {3, -1.5, 0.75}]

EDIT: I recommend that you experiment with different settings for PlotTheme to determine which is best for your classroom and smartboard.

Manipulate[
 Plot3D[y, {x, 0, 1}, {y, 0, 1},
  RegionFunction -> 
   Function[{x, y, z}, 
    x^2 + y^2 <= 1 && x >= 0 && y >= 0 && z >= 0],
  Filling -> 0,
  FillingStyle -> Opacity[.75],
  PlotStyle -> Opacity[.5], 
  AxesLabel -> (Style[#, 18, Bold] & /@
     {x, y, z}),
  BoxRatios -> {1, 1, 1},
  ViewPoint -> {3, -1.5, 0.75},
  PlotTheme -> pt],
 {{pt, "Classic", "Plot Theme"},
  {"Business", "Classic", "Default",
   "Detailed", "Marketing", "Minimal",
   "Monochrome", "Scientific", "Web"}}]