Grade 6 Mathematics Geometry – 3-D Objects Notes
Mathematics — Geometry
Subtopic: 3‑D Objects (Age 11 — Kenya)
3‑D (three‑dimensional) objects are shapes that have length, width and height (or depth). We see them every day: a shoe box, a water drum, a ball, or the roof of a house.
Important words
- Face — a flat surface on a 3‑D object (e.g., each side of a cube).
- Edge — a line where two faces meet (e.g., corner lines of a box).
- Vertex (vertices) — a point where edges meet (a corner point).
- Curved surface — a rounded surface (e.g., a ball or cylinder side).
Common 3‑D objects and their parts
All faces are squares and the same size.
- Faces: 6
- Edges: 12
- Vertices: 8
Faces are rectangles (may include squares).
- Faces: 6
- Edges: 12
- Vertices: 8
Two circular faces and one curved surface.
- Faces: 2 (circles)
- Edges: 0 (no straight edges)
- Curved surface: yes
Completely round — no faces, edges or vertices.
- Faces: 0
- Edges: 0
- Vertices: 0
Has triangular faces meeting at a top point.
- Example: square pyramid — 5 faces, 8 edges, 5 vertices
Nets — flat patterns of 3‑D objects
A net is what you get when you cut and open a 3‑D object so it lies flat. Nets help us find surface area.
(Fold the squares to make a cube)
(Two circles + one rectangle)
Simple formulas to remember
Use measurements in cm or m. For school problems use π ≈ 3.14 when needed.
- Cube (side = s): Volume = s × s × s = s³. Surface area = 6s².
- Cuboid (length l, width w, height h): Volume = l × w × h. Surface area = 2(lw + lh + wh).
- Cylinder (radius r, height h): Volume = π r² h. Curved surface area = 2π r h.
- Sphere (radius r): We only need to recognise it. (Advanced: Volume = 4/3 π r³.)
Worked example (simple)
A sugar tin is a cuboid with length 20 cm, width 10 cm and height 8 cm. Find the volume.
Volume = l × w × h = 20 × 10 × 8 = 1600 cm³.
Practice questions
- Name three 3‑D shapes you see at home and state one face or curved surface each has.
- A cube has side 4 cm. How many vertices does it have? What is its volume?
- A water drum is a cylinder with radius 21 cm and height 60 cm. Using π = 3.14, find its approximate volume (leave answer in cm³).
- Draw (on paper) the net of a cube and label one face “top”.
Answers (check yourself)
- Q2: Cube vertices = 8. Volume = 4³ = 64 cm³.
- Q3: Volume = π r² h = 3.14 × 21² × 60 ≈ 3.14 × 441 × 60 = 3.14 × 26460 ≈ 83104.4 cm³.
- Other answers will vary for Q1 and Q4 (use your own examples and drawing).
Tips for learning
- Count faces, edges and vertices on real objects (shoe box, cereal box, ball, water drum).
- Use nets to help find surface area — cut and fold paper to make the shape.
- Always write units (cm³, m³) in answers.
Good luck — practise with objects you find at home and in school. Maths is everywhere!