Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Mensuration
Compound Shapes and Parts of Shapes
What is Compound Shapes and Parts of Shapes?
A compound shape or solid is one built from, or left over from, shapes whose measurements are already known. Its area or volume is found by splitting it into non-overlapping known parts and adding, or by enclosing it in a complete shape and subtracting the part that is missing. Its perimeter is traced around the outside boundary only, and internal cutting lines are excluded. For a compound solid the volumes of the parts simply add, but the surface areas do not: a face where two parts are joined lies inside the solid and is excluded from the external surface area, while a face newly exposed by a cut must be included. A frustum is the solid left when a cone is cut parallel to its base and the top removed; the removed cone is similar to the complete cone, so the height scale factor gives every missing radius and slant length, and the frustum is found by subtracting the small cone from the complete one.
This definition is part of the Mensuration chapter in Cambridge O Level Mathematics (Syllabus D).