ConceptGeometry & Algebra
← All conceptsSolid geometry
solids, surfaces, volumes
12 ways this goes wrong. Each one is a named misconception the questions are built to catch.
- Cut-off ratio wrong referenceCompares a cut-off corner volume to the whole solid instead of to the remaining part.→
- Equilateral-triangle area sqrt3 missingDrops the sqrt3 factor in an equilateral-triangle base area.→
- Frustum vs prism formulaUses a prism formula where the frustum (averaged-base) formula is needed.→
- Impossible cross-section assumedAssumes a cross-section polygon the solid's faces cannot actually produce.→
- Inner solid not subtractedTreats a rotated annulus/ring as a full disk, forgetting to subtract the inner solid.→
- Inscribed vs circumscribed sphereConfuses inscribed-sphere inradius with circumscribed-sphere radius.→
- Lateral vs total surface areaComputes total surface area when only lateral (curved) is required, or vice versa.→
- Oblique-projection area ratioForgets the sqrt2/4 oblique-projection area ratio, or applies it to the side instead of the area.→
- Sector-angle to base-radius wrongRelates the unrolled-sector central angle to the r/l ratio (arc length vs radius) incorrectly.→
- Slant height vs height confusedUses the slant height as the cone/frustum vertical height (or as the radius) or vice versa.→
- Sphere uses wrong diagonalUses a face diagonal instead of the space diagonal for a circumscribed-sphere diameter, or forgets to halve it.→
- Tetrahedron volume factor wrongForgets the 1/6 (scalar triple product) or 1/3 (base x height) factor for a tetrahedron/pyramid.→
