What Is the Area of One Slice?

You'll learnto build a volume as an integral of one slice's area, to take the slice's side from the distance between two boundaries rather than from one curve, and to keep a square, a scaled rectangle and a fixed-height rectangle apart.

A solid on a flat base, sliced straight across, is just an integral of one slice's area. Two things have to be right: how long the slice's base is, and what the named shape does with that length. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · THE SIDE IS A DISTANCE, THEN THE SHAPE IS A FORMULA · v2

The side is the gap between two boundaries, then the shape is a formula

Before you start

What you're looking at

Two pictures of one slice. On the left is the solid's flat base seen from above, with the slice's footprint marked; on the right is that slice itself, face on.

The question

How long is the segment the base cuts out here, and what area does the named shape have on it?

Step 1 / 12