1
Volume of a cuboid: length times width times height
Discover Mathematics P6: Term 2, Unit 13, Lessons 3–4
GoalFind the volume of a cuboid by counting unit cubes and with length × width × height.
New words
volume · the amount of space a solid takes upunit cube · a cube with edges of 1 unit; 1 cm³ is a cube of edge 1 cmlayer · one flat level of unit cubes
Explanation
Volume is counted in cubes. A cuboid 5 cm long, 3 cm wide and 4 cm high can be filled with unit cubes of 1 cm³. The bottom layer holds 5 × 3 = 15 cubes. There are 4 layers, so the cuboid holds 15 × 4 = 60 cubes. Its volume is 60 cm³. This is the same as length × width × height. So volume of a cuboid = l × w × h. The unit is cubic: cm³ or m³. Do not mix up the units: area is in cm² (flat), volume is in cm³ (space). If you know the volume and two of the sides, divide to find the third.
ƒFormula
Volume of a cuboid = l × w × h (in cm³ or m³)
Base area × height: layer × number of layers.
Worked examples
A cuboid is 5 cm by 3 cm by 4 cm. One layer: 5 × 3 = 15 cubes. Four layers: 15 × 4 = 60 cubes. Volume = 60 cm³.
A block is 6 cm long, 4 cm wide and 3 cm high. Volume = 6 × 4 × 3 = 24 × 3 = 72 cm³.
Finding a side. A cuboid has volume 96 cm³, length 8 cm and width 3 cm. The base is 8 × 3 = 24 cm². Height = 96 ÷ 24 = 4 cm.
Class activity
Build with cubes. Use sugar cubes, dice or small blocks to build two different cuboids with 24 cubes. Write the length, width and height of each, and check that l × w × h = 24 for both.
Practice
1
Find the volume of a cuboid 7 cm by 3 cm by 2 cm.
7 × 3 × 2 = 42 cm³.
2
Find the volume of a cuboid 10 cm by 5 cm by 4 cm.
10 × 5 × 4 = 200 cm³.
3
A cuboid has a bottom layer of 12 cubes and 5 layers. How many cubes in all?
12 × 5 = 60 cubes, so the volume is 60 cm³.
4
A cuboid has volume 96 cm³, length 8 cm and height 4 cm. Find the width.
8 × 4 = 32 and 96 ÷ 32 = 3 cm.
5
Rana says a box 4 cm by 3 cm by 2 cm has volume 24 cm². What is wrong?
Volume is measured in cubic units. The answer is 24 cm³.