Deform a quadrant of a cylinder along the z-axis File Trim.blend shows an embellished quadrant of a vertical cylinder which is roughly 22 mm radius and 30 mm tall.  I need to deform it so that the bottom of the cylinder is about 30 mm radius, with the radius of increasing slowly at the top and more rapidly as the bottom nears.   I've tried extrusion and scaling and looked at suggested relevant questions, but haven't seen (or maybe understood) how to carry this out. The relevant objects in Layer 1 are CubeW and Cyl219W.
 1. How about some variation of proportional edit falloff.
 2. TIA for suggestions. 


https://www.dropbox.com/s/gy6e0cyhe59ghhr/NTrim.blend?dl=0
If you want a very smooth quadrant you will need more vertex density.  You know a smooth human face with many contours requires many more vertices than a simple cube
Edit Mode
Loop cut can do this.Control R
You can set the cursor to the center of a completed cylinder .. as if you had 4 quadrants.  You probably have seen Cylinder and Cones being edited which have complete circles so Blender can figure out center easily.  You need this one extra step since you only have one quarter circle.
Set cursor . Shift S .Set the center of scale for proportional editing to cursor.  This allows you to change shape from any point you choose.  This item is two UI boxes to the left of [edit mode] on the bottom strip of 3D View Window in your images above
Select bottom of quadrant. Many vertices.
Enable Proportional edit. o. Scale to see effect. Use mouse wheel.
Experiment many more times
State whether or not you are making progress
Tutorial https://www.youtube.com/watch?v=MrNVVHdKd3E