Common Solids
4.0 Geometry · 4.4 Common Solids
Syllabus tag: Kenya CBC | Grade 8 Mathematics | Strand 4.0 Geometry | Sub-Strand 4.4 Common Solids (16 lessons)
Lesson objectives
By the end of this sub-strand, you should be able to:
- Identify common solids and sketch their nets
- Work out surface area of solids from their nets
- Determine the distance between two points on the surface of a solid
- Make models of hollow and compact solids
Common Solids
A solid takes up space. A tin, a brick, a tent and a ball are all solids. Each has a name, a set of faces, and a way of being unfolded flat.
a) Naming solids
| Solid | Faces | Notes |
|---|---|---|
| Cube | 6 squares | all edges equal |
| Cuboid | 6 rectangles | three matching pairs |
| Cylinder | 2 circles, 1 curved | a tin |
| Cone | 1 circle, 1 curved | a funnel |
| Sphere | 1 curved | a ball |
| Triangular prism | 2 triangles, 3 rectangles | a tent |
| Pyramid | 1 base, triangles meeting at a point |
A face is a flat surface. An edge is where two faces meet. A vertex is a corner where edges meet.
A cuboid has 6 faces, 12 edges and 8 vertices. Count them on a box to be sure.
b) Nets
A net is the solid unfolded flat. Cut along enough edges and a box opens out into one flat shape.
Every face of the solid appears once in the net, at its true size.
A net folds back into the solid, so the faces must be in positions that allow that. Sketch one, cut it out, and fold it to check.
The same solid can have more than one correct net. A cuboid has several, and all of them are right as long as they fold up.
c) Net of a cylinder
A cylinder unrolls into two circles and one rectangle.
The rectangle is exactly as long as the circle is round. Its length is the circumference, 2πr.
That single fact is why the curved surface area of a cylinder is 2πr × h.
d) Surface area from a net
The surface area is the total area of every face. A net makes this easy, because every face is visible and flat.
Work through the net face by face, in pairs where the solid has pairs, and add.
Marking each face on the net as you use it stops you counting one twice or missing one.
e) Distance across a surface
Sometimes you need the shortest distance between two points on the surface, not straight through the solid.
An ant walking from one corner of a box to the opposite corner cannot go through the box. It must travel across the faces.
Unfold the solid into its net, mark both points, and join them with a straight line. That straight line on the flat net is the shortest path across the surface.
Measure it on the net, and that is the answer.
f) Hollow and compact solids
A hollow solid is empty inside, like a tin or a box. What matters is the surface.
A compact solid is solid throughout, like a brick or a ball of clay. What matters is the volume.
Making models from card gives hollow solids. Making them from clay gives compact ones.
g) Where this is used
A packaging designer draws nets to cut card efficiently. A tinsmith works out the sheet needed for a jerrican. A builder counts bricks by volume, not surface.
Words to know
- Net -- the two-dimensional shape formed by unfolding a solid so every face lies flat, connected in one piece.
- Hollow solid -- a solid with an empty interior, such as a container.
- Compact solid -- a solid that is filled throughout, with no hollow interior.
:::checkpoint Check yourself
- How many faces, edges and vertices does a cuboid have?
- What shapes make up the net of a cylinder?
- Why is the rectangle in a cylinder's net 2πr long?
- Find the surface area of a cube of side 6 cm. :::
Bridge to practice
Try the exercises below -- on nets of common solids, surface area from nets, and distances on a solid's surface.