Volume is how many unit cubes fill it
Fill a box layer by layer. One layer holds length times breadth cubes, and there are as many layers as the height. Volume is measured in cubic units, like cm³.
Class 4 to 10 · 170 games
Surface area and volume, explained with pictures
How much a solid holds, and how much it takes to wrap it.
In everyday life: A water tank to fill, a gift box to wrap, a tin of oil, an ice-cream cone.
Surface area is the wrapping
Open a box out flat and you get its net. The surface area is the area of every face added up, in square units. It does not tell you how much the box holds.
The same volume can need different wrapping
Two boxes can hold exactly the same 24 cubes and still need different amounts of paper. The long thin one needs more. Volume and surface area are different things.
A curved surface unrolls flat
Peel the label off a tin and it is a rectangle as tall as the tin and as wide as the tin is round. A cone unrolls into a slice of a circle.
A worked example
A box is 5 cm long, 4 cm wide and 3 cm tall. What is its volume and its surface area?
Volume 60 cm³. Surface area 94 cm².
One layer is 5 × 4 = 20 cubes and there are 3 layers, so 60. The faces are 20, 15 and 12 square cm, each twice: 2 × 47 = 94.
Words to know
- volume
- How much space a solid takes up, counted in unit cubes.
- surface area
- The area of all the faces of a solid added up.
- net
- A solid opened out flat, so all its faces can be seen at once.
- slant height
- The length down the sloping side of a cone, not the height straight up.
In the games
You will fill boxes layer by layer, unfold them, pour a cone into a cylinder, and scale a solid to see what happens to its area and volume.
Skills
- Volume of a cuboid, counted in layers · Class 5
- Nets of a cube, and views of a stack · Class 5
- Unfold a box to find its surface area · Class 6
- Same volume, different wrapping · Class 6
- Litres and cubic centimetres · Class 6
- Faces, edges and corners · Class 7
- A painted cube, cut up · Class 7
- Volume of a prism: base times height · Class 7
- Surface area and volume of a box and a tin · Class 8
- Double the sides: what happens to area and volume · Class 8
- Cones, spheres and hemispheres · Class 9
- Surface area and volume of combined solids · Class 10
- The frustum of a cone · Class 10
By class
Class 4 surface area and volume (3) · Class 5 surface area and volume (20) · Class 6 surface area and volume (25) · Class 7 surface area and volume (25) · Class 8 surface area and volume (45) · Class 9 surface area and volume (30) · Class 10 surface area and volume (22)
Practise surface area and volume in Tivumo
No download, no account for your child. Classes 3 to 12, more than 1,100 games.