Solids and circle vocabulary
Name faces, edges, cross-sections and the parts of a circle before calculating with them.
Core and Extended.
Before you begin
- Recognise triangles, quadrilaterals and perpendicular lines.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How many faces does a cube have?
What you will learn
- Distinguish common solids and their surfaces.
- Identify chords, tangents, arcs, sectors and segments.
- Explain why a diameter is a special chord.
Describe a solid
A cube has six square faces; a cuboid has six rectangular faces. A prism has a uniform cross-section along its length: a triangular prism has two matching triangular ends and three rectangular side faces when it is a right prism. A pyramid joins a polygonal base to one apex with triangular faces. Faces are flat surfaces, edges join surfaces, and vertices are corners.
A cylinder has two parallel circular ends and a curved surface. A cone has one circular base, a curved surface and an apex. A sphere has one curved surface; a hemisphere is half a sphere with a circular flat base. A frustum is the part of a cone or pyramid left after cutting off its top parallel to the base. State whether you mean a flat face or a curved surface when describing a solid.
Separate the parts of a circle
The radius joins the centre to the circumference. A diameter passes through the centre between two circumference points and has length twice the radius. A chord joins any two circumference points; a diameter is the longest chord. A tangent touches the circle at one point, whereas a secant crosses it at two points.
An arc is part of the circumference. Two endpoints usually define a shorter minor arc and a longer major arc. A sector is bounded by two radii and an arc, like a slice; a segment is bounded by a chord and an arc. A semicircle is half the circle cut by a diameter. Identify the boundary before deciding whether a shaded region is a sector or a segment.
Pause and explain
Which boundary describes a sector?
Worked example
A circle has radius 7 cm. A shaded region is bounded by a chord and its minor arc. Name the region and give the diameter.
Show the worked solution
- A chord with an arc bounds a segment, rather than a sector.
- The shorter arc makes this the minor segment.
- The diameter is twice the radius: 2 × 7 = 14 cm.
Answer Minor segment; diameter 14 cm.
From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
List the faces of a right triangular prism and explain why it is not a triangular pyramid.
Give me a hint
Compare its ends with a pyramid's apex.
Compare my reasoning
- There are two matching triangular ends.
- Three rectangular faces join the corresponding sides.
- A pyramid has one base and an apex; this solid keeps the same triangular cross-section.
Two triangles and three rectangles; a uniform cross-section, not one apex.
Look for these in your work
- Counted both end faces.
- Used the solid's defining property.
A chord goes through a circle's centre. The circle has diameter 18 cm. Name the chord and find the radius.
Give me a hint
The centre condition distinguishes this chord.
Compare my reasoning
- A chord through the centre is a diameter.
- A radius is half the diameter.
- 18 ÷ 2 = 9 cm; include the length unit.
Diameter; radius 9 cm.
Look for these in your work
- Applied the centre condition.
- Halved rather than doubled the given diameter.
A lampshade is made by cutting the top off a cone parallel to its base. Name the remaining solid and describe its two ends.
Give me a hint
The cut creates a smaller parallel circular end.
Compare my reasoning
- The remaining solid is a conical frustum.
- Its large and small ends are parallel circles.
- A curved surface joins them; the cone's original apex has been removed.
A conical frustum with two parallel circular ends of different sizes.
Look for these in your work
- Used the term frustum accurately.
- Distinguished the remaining solid from a complete cone.
Common mistakes
- Counting edges instead of faces.
- Confusing a sector with a segment.
- Calling any line near a circle a tangent without the one-point contact condition.
What can you explain now?
Does every chord pass through the centre?
Compare with the explanation
No; only a diameter does.
A chord requires two endpoints on the circumference, without requiring the centre to lie on it.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Sketch and label a chord, a diameter, a tangent, a sector and a segment tomorrow. Describe one prism and one pyramid aloud.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.
Original StudyForA teaching content · AI-assisted checks · Human teacher review pending.
Number contains 19 sequenced lessons; Algebra and graphs 21; Coordinate geometry 10; Geometry 15; Mensuration 13; Trigonometry 13; Transformations and vectors 11; Probability 7; Statistics 13. All 72 syllabus section entries now link to teaching and staged practice. Seven mixed checkpoints sample skills and suggest review lessons. Nine earlier overviews remain available. Full cumulative assessment and human teacher review remain pending. Written lesson practice, charts and constructions are self-checked, not automatically graded. Checkpoints do not save an exam grade or certify mastery.
Check the official syllabus 2025–2027 Open related practice and resources