1. Volume Of Solids And Liquids
Primary 6 Mathematics

2. Chapter Learning Outcomes
Find an edge of a cuboid/rectangular tank given its volume and the other measurements (2 other edges or area of one face/base)
Use calculator to find square root/cube root
Find one side of the square base of a cuboid/tank given volume and height
Find one edge of a cube/cubical tank given volume
Find volume of water and/or height of water level in cuboid/rectangular tank

3. Volume Of Solids - Cube How can you find the volume of a cube?
Volume = Length  Breadth  Height
Remember that a cube has the
same length, breadth and height.

4. Volume Of Solids - Cuboid
How can you find the volume of a cuboid?
Volume = Length  Breadth  Height

5. Finding edge of a cuboid
If two of the edges of a cuboid and its volume is given, you can find the value of the third edge.

6. Example
A cardboard box has a volume of 225 cm2. If the box has a length of 15 cm and breadth of 3 cm, find its height.
Volume = length  breadth  height
15 cm  3 cm  height = 225 cm2
Therefore:
Height = 225  (15  3) = 5 cm

7. Finding edge of a cuboid
If the base area or area of one face of a cuboid and its volume is given, you can find the value of the third measurement.

8. Example
A fish tank has a base area of 126 cm2. If its capacity is litres, find its height.
Capacity of tank = litres = 1638 cm3
Capacity of tank = length  breadth  height
= base area  height
Therefore, height = capacity  base area
Height of tank = 1638  126 = 13 cm

9. Finding Square Root
To find the area of a square, we calculate Side  Side.
If the area of a square is given, we can find the length of the side using square root.

10. Example
Find the square roots. 5
9 m
25 cm

11. Example
A metal tank with a square base has a volume of 3630 cm2 and a height of 30 cm. What is the length of its base?

12. Finding Cube Root
To find the volume of a cube, we calculate Edge  Edge  Edge.
If the volume of a cube is given, we can find the length of the edge using cube root.

13. Example
Find the cube roots. 4
11 cm
23 m

14. Example
A plastic cube has a volume of 2744 cm3. Find the length of one edge of the cube.

15. Volume Of Liquids
We can measure volume of liquids using millilitres (ml) or cubic centimetres (cm3).
Using the formulas shown so far, we can solve word problems involving volume of liquids.
1 cm3 = 1 ml

16. Example
A cubical fish tank is 1/4-filled with 128 ml of water. What is the length of each edge of the tank?

17. Example
An empty rectangular tank measuring 50 cm by 20 cm by 16 cm is being filled with water flowing from a tap at 8 litres per minute. How long will it take to fill the tank to its brim?

18. Reference - Textbooks Learning Outcomes 6B p. 98–107 6B p.56–60
Find an edge of a cuboid/rectangular tank given its volume and the other measurements (2 other edges or area of one face/base)
6B p. 98–107
6B p.56–60
Use calculator to find square root/cube root
Find one side of the square base of a cuboid/tank given volume and height
Find one edge of a cube/cubical tank given volume
Find volume of water and/or height of water level in cuboid/rectangular tank
6B p.110–115
6B p.61–68