Solid Geometry Revision

≈ 40 min

Solid Geometry Revision

CAPS Grade 12 explicitly revises Grade 11 solid geometry, because everything in Term 3 — interpenetration, developments — rests on it.

The four ideas that carry everything:

A face shows true shape only when parallel to the projection plane. Every true-shape and auxiliary-view problem is this one fact.
A line shows true length only when parallel to the projection plane. If it is inclined to both, neither view gives it, and it must be rotated.
Solids are described by their axis relative to the HP and VP. State that first, and the views follow.
Curved surfaces are handled with generators. Divide, project, work one at a time, join in order.

Convention. Solid geometry is first angle: plan below elevation, side view on the opposite side to the direction of viewing.

Worked example. "Find the true shape of the section" and "find the true length of the edge" are the same problem in different dress: both need a view taken square to the thing being measured.

Core checkpoint: True shape and true length both require a view parallel to what you are measuring. Almost every solid geometry question reduces to arranging that.

What single condition is required for both true shape and true length?

The face or line must be parallel to the projection plane of the view.

It must be perpendicular to the projection plane.

It must lie on the ground line.

The solid must be standing on the HP.

Which convention does solid geometry use?

First angle — plan below the elevation.

Third angle — plan above the elevation.

Either, at the draughtsperson's choice.

Isometric.

How are curved surfaces handled in solid geometry problems?

With generators — divide, project, work one at a time, and join in order.

By calculating the curve's equation.

By sketching the curve freehand between known points.

Curved surfaces are excluded from solid geometry.

Why is learning each solid geometry problem as a separate procedure a weak strategy?

They are four ideas recombined — holding the ideas lets you reconstruct any procedure, while memorised procedures fail on unfamiliar phrasing.

Because there are too many procedures to memorise.

Because procedures change between examinations.

It is not weak — memorising procedures is the most reliable method.