الأسبوع 26 · المجسّمات وقياس الحجم بالمكعبات · 3 دروس
1
Solid shapes: dimensions, volume and capacity
Discover Mathematics P5: Term 2, Unit 11, Lessons 1–3
GoalName solid shapes by their faces and vertices, and tell the difference between volume and capacity.
New words
solid · a three-dimensional shape that takes up spaceface · a flat or curved surface of a solidvolume · the amount of space a solid takes upcapacity · how much a container can hold, in mL or L
Explanation
A solid has three dimensions: length, width and height. The main solids are the cube, the rectangular prism (a box), the square pyramid, the cylinder, the cone and the sphere. We tell them apart by their faces and vertices. A cube has 6 flat square faces and 8 vertices (corners). A rectangular prism also has 6 flat faces and 8 vertices, but its faces are rectangles. A square pyramid has 5 flat faces and 5 vertices. A cylinder has 2 flat circles and 1 curved surface and no vertices. A cone has 1 flat circle, 1 curved surface and 1 vertex. A sphere has only a curved surface. Volume and capacity are both about “how much”. Volume is the space the solid itself takes up, measured in cubic units. Capacity is how much a container can hold, measured in millilitres and litres. A full 1-litre bottle has a capacity of 1 litre, and the plastic of the bottle has its own small volume.
Solid
Flat faces
Curved surfaces
Vertices
Cube
6
0
8
Rectangular prism
6
0
8
Square pyramid
5
0
5
Cylinder
2
1
0
Cone
1
1
1
Sphere
0
1
0
Worked examples
A game die has 6 equal square faces and 8 corners. It is a cube. A tin of beans has two flat circles and a curved side: a cylinder. A football is a sphere: no flat faces and no corners.
A party hat has one flat circle, one curved surface and one point, so it is a cone. The pyramids of Giza are square pyramids: a square base and 4 triangle faces, which makes 5 faces and 5 vertices.
A water bottle says 1.5 L. This is its capacity: how much water it can hold. The space taken up by the whole bottle on the shelf is its volume. A good fact: 1 millilitre of water takes up 1 cubic centimetre, so 1 litre takes up 1,000 cubic centimetres.
Class activity
Solid hunt. Collect five objects from home or school (a tin, a die, a ball, a tissue box, a party hat or paper cone). Sort them into groups by their shape. For each, count the flat faces and the corners and fill in a table. Then fill a cup and a small bottle with water: which can hold more? That is capacity.
Practice
1
A solid has 6 square faces that are all the same. What is it?
A cube.
2
Which solid has 2 flat circles, 1 curved surface and no vertices?
A cylinder.
3
How many vertices does a square pyramid have?
5: four corners of the base and one at the top.
4
Is it volume or capacity? (a) How much juice a carton holds. (b) The space a brick takes up.
(a) Capacity. (b) Volume.
5
Name the solid shape of: a tin of tuna, a tissue box, an orange.
