3D shapes and their names

A 3D shape, or solid, is a shape you can pick up and hold, like a box, a ball or a tin. Each one has a name, and you do not need to guess it. Look at its faces, the flat or curved surfaces on the outside, and the name follows.

The rule

A solid is named by its faces. Check whether they are flat or curved, and look at the shape of the base. A pyramid rises from its base to a point. A prism keeps the same shape all the way through, from one end to the other.

How to name a solid

  1. Look at the surfaces. If it is curved all over, with no flat face at all, it is a sphere, like a ball.
  2. If it has curved and flat surfaces, count the flat circles. Two circles, one at each end, make a cylinder, like a tin. One circle and a point at the other end make a cone, like an ice cream cone.
  3. If every face is flat, look at the top. If the faces lean in and meet at a point, it is a pyramid. It is named after its base, so a square base makes a square-based pyramid.
  4. If the two ends are the same flat shape, joined by rectangles, it is a prism. It is named after its end, so triangle ends make a triangular prism.
  5. A box shape has six rectangle faces and is called a cuboid. If all six faces are squares of the same size, it is a cube.

Worked examples

What solid is this?

A cube. Every face is flat and square, and all the squares are the same size. You can see three faces here. The dashed lines are the edges at the back, which you cannot see but are still there. If the faces were rectangles, it would be a cuboid.

Which one is the cylinder, and which one is the cone?

The left one is a cylinder: a flat circle at each end and a curved surface joining them, like a tin of soup. The right one is a cone: one flat circle at the bottom, and a curved surface that comes up to a point, like a party hat.

Which one is the pyramid, and which one is the prism?

Both have triangles, so look at the ends. The left one is a pyramid: a square base, with four triangles leaning in to meet at one point. The right one is a triangular prism: the same triangle at the front and the back, joined by three rectangles, like a tent.

What solid is each of these everyday things?

a sugar cube → cube
a football → sphere
a tin of soup → cylinder
an ice cream cone → cone
a cereal box → cuboid
a tent → triangular prism

Spotting solids at home is good practice. A cereal box is a cuboid, not a cube, because its faces are rectangles of different sizes.

Cuboid or rectangular prism

British schools say cuboid for a box shape. In America it is usually called a rectangular prism, which is just as true, because a cuboid is a prism with rectangle ends. They are the same solid.

Pyramids and prisms come in more kinds than the two above. A triangular-based pyramid has a triangle for its base, so it is made of four triangles. A hexagonal prism, the shape of most pencils, has a hexagon at each end joined by six rectangles.

Why prisms and pyramids are named after one face

Slice a prism straight across, like a loaf of bread, and every slice is the same shape as its end. A triangular prism gives triangles all the way through, and a cuboid gives rectangles. So the end tells you the whole solid, and that is the face it is named after.

A pyramid is different. Slice it across and the slices get smaller as you go up, until there is only the point. Every slice is the same shape as the base, only smaller, so the base is the face that names it.

Curved surfaces explain how a solid rolls. A sphere rolls any way you push it. A cylinder rolls in a straight line, on its curved side. A cone rolls round in a circle, because its point stays in one place. Solids with only flat faces do not roll at all, they slide.

Where mistakes happen

Questions people ask

Is a cube a cuboid?

Yes. A cube is a special cuboid, one whose faces are all squares of the same size, in the same way that a square is a special rectangle.

Is a cylinder a prism?

Not at primary school. A prism has flat faces only, and a cylinder has a curved surface. Some older books call it a circular prism, because its slices are all the same circle, but most schools keep the two apart.

How many faces does a cube have?

Six, and they are all squares. It also has 12 edges and 8 vertices, or corners. Counting faces, edges and vertices shows how to count them without missing the ones at the back.

Is a 3D shape the same as a solid?

Yes. 3D shape is what most schools say now, and solid is the older word. Both mean a shape with length, width and height, not a flat one.