Wentworth's Plane and Solid Geometry · Table of Formulas, pp. 461–464 · Book 10: Book IX: Conic Sections
148. Review: the table of formulas
Goal: Your student reviews the formulas of plane and solid geometry from the book's own table and can say where each comes from.
You'll need
- The book, open to these pages
- A ruler (straightedge) and a pair of compasses
- Sharp pencil, eraser and plain paper (or a geometry notebook)
What's in the book
Pages 461–464: the Table of Formulas for plane geometry (line values and areas) and solid geometry (prisms, pyramids, cylinders, cones, the prismatoid, spherical areas and volumes, the ellipse), each with the page where it is proved.
The lesson, step by step
Warm up
Ask your student to say, without looking, the volume of a sphere, a cone and a cylinder.
Plane formulas
Read the plane-geometry part of the table together. For three or four of them, turn to the page given and find the proof.
Solid formulas
Read the solid-geometry part. Your student groups the formulas into families: prism and cylinder (B × H), pyramid and cone (⅓ B × H), frustums, sphere.
One formula for many
Ask: Which single formula covers prism, pyramid, frustum, cylinder and cone? (The prismatoid formula, ⅙H(B + b + 4M).)
Test yourself
Cover the formulas and let your student write them out; then check.
Wrap up
The book is finished. Celebrate!