Grade 5 Mathematics Geometry – 3-D Objects Notes
Mathematics — Geometry
Subtopic: 3‑D Objects (for age 10, Kenya)
A 3‑D object (three‑dimensional object) is a shape that has three measurements: length, width and height (or depth). These objects take up space. Examples you see every day are boxes, balls and cans.
Common 3‑D shapes
- Cube — all sides are equal (like a dice).
- Cuboid — like a shoe box (different length, width, height).
- Sphere — perfectly round (like a ball).
- Cylinder — like a tin can (two circular faces and one curved face).
- Cone — like an ice‑cream cone (one circular base and a curved surface).
- Pyramid — a flat base and triangular faces meeting at a point (like some monuments).
Faces, Edges and Vertices
- Face: a flat surface on a 3‑D object (a plane).
- Edge: where two faces meet (a straight line).
- Vertex (plural: vertices): a corner where edges meet (a point).
Examples: A cube has 6 faces, 12 edges and 8 vertices. A cylinder has 2 circular faces and 1 curved face. It does not have vertices.
Look at a dice. Count the faces (flat sides), then count the edges and the corners (vertices).
Volume (number of cubic units)
Volume tells how much space an object holds. For learners aged 10 we start with cubes and cuboids:
- Cube: volume = side × side × side = side³
- Cuboid (rectangular box): volume = length × width × height
A school box measures 4 cm by 3 cm by 2 cm. What is its volume?
Volume = length × width × height = 4 cm × 3 cm × 2 cm = 24 cubic cm (24 cm³).
Simple activities (Kenyan classroom / home)
- Collect 5 objects (e.g. ball, book, tin, pencil box, roof tile). Name the 3‑D shape for each.
- Pick a cuboid (shoe box). Measure length, width, height with a ruler and calculate its volume.
- Draw the net of a cube: make 6 equal squares so you can fold them and make a cube.
Practice questions
- How many faces, edges and vertices does a cube have?
- A rectangular tank is 5 m long, 2 m wide and 1 m high. What is its volume? (Answer in cubic metres)
- Which of these objects has no vertices: ball, box, cone, pyramid?
- Draw a net (on paper) and fold it to make a cube. How many squares did you use?
Answers (click to show)
- Cube: 6 faces, 12 edges, 8 vertices.
- Volume = 5 × 2 × 1 = 10 m³.
- The ball (sphere) has no vertices. A cone also has no vertices (it has 1 vertex/point at the top depending on how you define it; commonly the cone has 1 vertex). Note: a cone has 1 vertex, a sphere has 0.
- You use 6 squares for a cube net.
Tip for teachers & parents: Use local examples — match shapes to everyday items (mango = sphere, sugar packets = cuboid). Encourage learners to touch and count edges and faces to build understanding.