Flat shapes and solid shapes
A square drawn on paper is flat. It has a length and a width, and nothing more. A solid shape takes up space: you can pick it up, hold it and turn it round. Each flat surface on a solid is called a face.
A cube is a solid with 6 flat faces, and every face is a square. A dice is a cube. Count the faces in pairs: the top and the bottom, the front and the back, the left and the right. That is 2 + 2 + 2 = 6 faces.
The 6 faces of a cube are numbered. The gold numbers are on the 3 faces you can see, and the gray numbers are on the 3 faces on the far side.
A solid with no flat face
A sphere is a solid ball. Its surface is curved all over, so however you turn it, no part of it is flat. A ball and an orange are both spheres.
A circle is not a sphere. A circle is flat, like a coin drawn on paper. A sphere takes up space.
A sphere is round all over and has no flat face.
Flat circles and a curved side
A cylinder has a flat circle at each end and one curved side that wraps round between them. It is the same width all the way up. A tin of soup is a cylinder.
A cone has one flat circle at the bottom. Its curved side narrows as it rises, all the way to a single point at the top. A party hat is a cone.
To tell the two apart, look at the top. A cylinder is flat on top, the same as underneath. A cone has a point.
A cylinder: a flat circle at each end, and one curved side between them.
A cone: one flat circle at the bottom, rising to a single point.
The faces decide the name
A solid is named by its faces, not by its size or its color. A small dice and a big toy block are both cubes, because every face of each one is a square.
The faces also tell you what a solid can do. A solid with a curved face can roll: the sphere, the cylinder and the cone. A solid that is flat on the top and flat on the bottom can stack, one on another: the cube and the cylinder. Nothing rests on the point of a cone.
Worked example: Kitchen Things Sorted into Cylinders, Spheres, Cubes and Cones
Question Dad puts 7 things on the kitchen table: 1 can, 1 ball, 1 orange, 3 dice and 1 party hat. A can is a cylinder. A ball and an orange are spheres. A dice is a cube. A party hat is a cone. (a) How many spheres are on the table? (b) How many things are cylinders or cubes?
1.Draw the 7 things: 1 can, 1 ball, 1 orange, 3 dice and 1 party hat.
There are 7 things on the table: 1 can, 1 ball, 1 orange, 3 dice and 1 party hat. 2.Make a pile for each solid shape. The can is a cylinder. The ball and the orange are spheres. The 3 dice are cubes. The party hat is a cone.
Make a pile for each solid shape. The can is a cylinder. The ball and the orange are spheres. The dice are cubes. The party hat is a cone. 3.(a) Count the pile of spheres: 1 + 1 = 2. There are 2 spheres on the table.
(a) Count the pile of spheres: 1 + 1 = 2. There are 2 spheres on the table. 4.(b) Add the cylinder and the cubes: 1 + 3 = 4. There are 4 things. Check: 1 + 2 + 3 + 1 = 7 things.
(b) Add the cylinder and the cubes: 1 + 3 = 4 things. Check: 1 + 2 + 3 + 1 = 7 things.
Answer: (a) 2 spheres; (b) 4 things
Common mistakes
- Counting only the ball as a sphere. An orange is round all over like a ball, so it is a sphere too.
- Calling the can a cone. A cone has a point at the top. A can is flat at the top and flat at the bottom, so it is a cylinder.
More shapes and where they sit problems, worked step by step →
Worked example: Solid Shapes That Can Roll and Solid Shapes That Can Stack
Question Sam has 6 things: a ball, an orange, a can, a dice, a brick and a party hat. The ball and the orange are spheres. The can is a cylinder. The dice is a cube. The brick is a cuboid. The party hat is a cone. (a) How many of the things can roll? (b) How many of the things can stack, one on top of another?
1.A solid shape can roll when it has a curved face. The sphere, the cylinder and the cone each have a curved face.
A solid shape can roll when it has a curved face. The sphere, the cylinder and the cone each have a curved face. 2.(a) Count the things that roll: the ball, the orange, the can and the party hat. 4 things can roll.
(a) The ball, the orange, the can and the party hat can roll. That is 4 things. 3.A solid shape can stack when it is flat on the top and flat on the bottom. The cylinder, the cube and the cuboid are flat on the top and on the bottom.
A solid shape can stack when it is flat on the top and flat on the bottom: the cylinder, the cube and the cuboid. 4.(b) Count the things that stack: the can, the dice and the brick. 3 things can stack. The can is in both counts, because a cylinder can roll and stack.
(b) The can, the dice and the brick can stack. That is 3 things. The can is in both counts.
Answer: (a) 4 things; (b) 3 things
Common mistakes
- Leaving the party hat out of the things that roll. A cone has a curved face, so it rolls on its side.
- Counting the party hat as a thing that can stack. A cone has a point on the top, so nothing can rest on it.
More shapes and where they sit problems, worked step by step →