Solids: cube, sphere, cylinder

What you hold in your hand is not flat. You will spot a cube, a sphere, a cylinder and a cuboid.

Shapes you can pick up

You cannot pick up a square on paper. But you can pick up a dice. Things that have height, width and depth are called solids.

A cube (maths people also say it that way) has six same square faces. A dice, a Rubik’s cube.

A cuboid is a stretched cube: a shoe box, a brick, a book.

A sphere is perfectly round from every side. A ball, a globe.

A cylinder has two round ends and a curved side. A tin, a toilet-roll tube, a pot.

Look around the room. A toy box, a ball under the bed, a mug on the table, a sugar cube in the kitchen. All solids. All day you pick them up — and today you will start to call them by the right names. And you will learn to spot them even with your eyes shut, just by touch.

A shape from paper is flat. A solid is a thing. A flat shape has sides, a solid has faces, edges and corners. Today you will learn to tell them by touch and by eye.

Sofie ties a scarf over Filip’s eyes. “Guess what you are holding!” She hands him a tin. Filip feels: “Two flat round ends… curved sides… a cylinder! Is it a tin?” A point. Next thing: all flat faces, all the same, sharp edges. “A cube!” It is a dice from Ludo. Then a little ball — “a sphere, that’s easy.” At last a tea box: flat faces, but some longer. “A cuboid!” Filip guesses even without eyes. Solids can be spotted with hands. Then they swap. Sofie knows everything except a matchbox — a cuboid like a cube, who can tell. Filip hints: “Compare the faces!”

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Does it roll every way? A sphere. Does it roll only on its side? A cylinder. Does it not roll at all and has flat faces? A cube or a cuboid.

How to spot a solid

A spotting method, even with your eyes shut:

1. Does it roll? Put the solid on the table and give it a push.

It rolls any way → a sphere. It is round from every side.
It rolls only one way (on its side) → a cylinder. Stood on its end it stands, laid down it rolls.
It does not roll → it has flat faces, go to step 2.

2. Compare the faces.

All six faces are the same squares → a cube.
The faces are rectangles, some longer → a cuboid.

A solid dictionary: a face is a flat surface (a cube has 6 of them). An edge is the line where two faces meet (a cube has 12 of them). A corner (vertex) is the point where edges meet (a cube has 8 of them). A sphere has no face, no edge, no corner — that is why it rolls so nicely.

Why does it matter? Builders know it exactly: walls are built from cubes and cuboids, because they sit on each other. You cannot build a wall from spheres — they roll away. A cylinder is good for columns and tins. The shape of a solid says what it is good for.

Cube or cuboid? A shoe box

The box does not roll — all flat faces. Cube or cuboid?

I compare the faces: the lid is a big rectangle, the sides are smaller. The faces are not the same.

It is a cuboid.

A cube would have all six faces completely the same — all squares. A shoe box does not have that, it is long. A sugar-cube box is often a cuboid too. The name does not always tell the truth, the shape never lies.

Why does a tin roll only on its side?

I stand the tin on its end: it stands. The end is flat and even, it holds it.

I lay it on its side: it rolls. The sides are curved, the wrap has no flat surface.

That is the sign of a cylinder: two flat ends and a curved wrap.

A sphere always rolls — it has no flat surface to stand on. That is why you cannot keep a ball on a slope, but you can keep a tin standing.

Count the faces of a dice

I take a dice and turn it. I count the faces with dots.

Top one, bottom a second. Four around: front, back, left, right.

Together 6 faces. Each is a square and all are the same size.

That is why a dice always lands with exactly one number up — each face has the same chance. If the dice were a cuboid, the big faces would land more often. The game would be unfair.

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Do not mix a flat shape and a solid: a square is drawn on paper, a cube is a thing in your hand. If you call a ball “a circle”, a maths person sits up. A ball is a sphere. A circle is its picture.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Start with ten. If it goes well, add more.

Spot the solid: cube, cuboid, sphere, cylinder.

Practise the questions

On paper

Paper, a pencil and a search trip around the flat.

Find one cube at home, one cuboid, one sphere and one cylinder. Write what you found.
Play guessing with your eyes shut with a parent: spot solids by touch and say how you knew.
Try rolling: which of the solids you found rolls any way, which only on its side, which not at all?
Count the faces of a box (a cuboid). There should be 6 of them.

Now you 💪

I know a cube, a cuboid, a sphere and a cylinder — even by touch.
I know what a face, an edge and a corner are.
I can say what rolls and why.

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Done when: You find all four solids at home and you spot them with your eyes covered.

What to take from this lesson

Solids have height, width and depth. You pick them up.
Cube: 6 same square faces. Cuboid: a stretched cube.
A sphere rolls any way. A cylinder only on its side.
A face is a surface, an edge is a line, a corner is a point.
A ball is a sphere, not a circle. A circle is flat.