Pick a standard setup. Only the boxes for that type appear: 2D lune is two circles (inside one, outside the other); 3D disk asks which surface and which disk; 3D ring asks which surface and which ring; between asks which two surfaces. The figure stays in 3D. Identify r, then θ, then h with dashed markers.
Standard setup
Which two circles · inside the first, outside the second
Inside (x − a)² + (y − b)² ≤ R²
Outside (x − a)² + (y − b)² ≥ R²
Which disk · (x − a)² + (y − b)² ≤ R²
Which ring · R₀² ≤ (x − a)² + (y − b)² ≤ R₁²
Which surface · under z = …
Which two surfaces · fill both
Allowed: pi, sqrt, sin, cos, r, theta, x, y.
Identify r
The 3D region stays. Dashed markers point out r, then θ, then h.
region
identify r, θ, h
surfaces
Move through the region
What this step is doing
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