When the Line Moves, the Radii Trade Places

You'll learnto measure both radii from the same shifted axis, to recognize that outer means farther rather than upper, to read a negative volume as a missed swap, and to test both radii where the boundaries meet.

Two radii, one line that is not a coordinate axis, and one fact that catches almost everybody: when the line sits beyond the region, the boundary that was on top becomes the inner radius. Outer means farther, and that stops meaning upper the moment the line moves. The quieter error is shifting one radius and leaving the other. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · BOTH RADII, SAME LINE, SAME FORM · v2

Both radii are distances from the same line, so outer means farther

Before you start

What you're looking at

A region between two curves and a dashed amber line above them that it is being spun about. Two radius segments start on that line, one reaching each boundary.

The question

Which of the two segments is longer? That boundary gives the outer radius, whether or not it is the upper curve.

Step 1 / 12