Derive the Constant, Do Not Recall It

You'll learnto build each cross-sectional area from the shape's own geometry, to tell a leg from a hypotenuse and a diameter from a radius in the wording, and to check a set of volumes against the heights of the shapes that produced them.

The method has not changed since Topic 8.7. What changes is the number that turns a base length into an area, and every one of them is worth deriving rather than recalling. Two of this topic's three commonest wrong answers are exactly double the truth, which is why nothing about them looks wrong. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · WHAT IS THE BASE TO THE SHAPE? · v2

The shape decides the constant, and the wording decides the shape

Before you start

What you're looking at

The same two panels as Topic 8.7. On the left, the base region with one slice's footprint; on the right, that slice face on, now a triangle or a semicircle rather than a square.

The question

What is that base segment to this shape: its side, a leg, the hypotenuse, a diameter, or a radius?

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