How to draw and fill the shaded region of the disk in Inkscape as shown in the image below?
Draw an ellipse, and duplicate it using Ctrl+D
Move it above the lower one (you can nudge it with the up arrow key on your keyboard)
With snapping enabled, draw a rectangle to intersect with the two ellipses (see example below)
With the select tool S hold down Shift and also select the bottom ellipse
Do Path > Union or use the shortcut Ctrl++, and set the fill to grey
Select the top ellipse and set the fill to white
Example showing steps 3 to 6