Volume and Capacity – Basic 5 Mathematics Lesson Note (Second Term)

Behavioural Objectives: By the end of this lesson, learners should be able to:

1. Define volume and capacity
2. Understand the difference between volume and capacity and state their relationship
3. Convert between the concept of capacity and apply it to real-life problems
4. Learn about cubic metre, cubic centimetre, litre, millilitre and gallon
5. Solve word problems

Volume and Capacity

Volume: Volume is the amount of space occupied by a three-dimensional object. It is measured in cubic units (like cubic metres, cubic centimetres) and it is about how much space a three-dimensional object takes up.

Capacity: Capacity is the maximum amount a container can hold. It is measured in litres (L) and millilitres (mL).

Units of Volume:

The standard units of volume of a shape, solids for length, with, and height (given: length × width × height = volume in cubic units)

Capacity: To find the capacity of a container (cup or water and measure how much it holds, Capacity can be measured in millilitres and litres as follows:

• 1 litre = 1000 millilitres
• 1000 litres = 1 cubic metre
• 1 cubic centimetre = 1 millilitre
• 1 gallon = 4.55 litres (gallon = gallon)

Volume Examples:

• Cube: Volume = side³ = s³ where s is the length of the side
• Cuboid: Volume = length × width × height
• Cylinder: Volume = πr²h = 3.14 × radius² × height

Remember volume is about how much space an object takes up, while capacity is about how much a container can hold.

Learning Examples:

Solving Problems:

Remember to follow the volume of cuboid is L × W × H where L is the length of the cuboid, W is the width of the cuboid and H is the height of the cuboid. The volume is usually given in cubic centimetres (cm³) or cubic metres (m³).

The formula for finding the volume of a cuboid is V = L × W × H where the volume is in the metric system. For example, if the length is 10 metres, the width is 8 metres and the height is 6 metres, then the volume will be 10 × 8 × 6 = 480 cubic metres.

The length unit are a dimensional concept. For example, a volume that measures 2 litres of volume can be equal to 2000 millilitres or 2000 cubic centimetres. This is because 1 litre = 1000 millilitres = 1000 cubic centimetres.

Volume Formula:

• Volume of a cube = side³ = s³ (where s is the length of the side of the cube)

Examples:

Volume Examples:

(1) Calculate the volume of a cuboid that has dimensions 10 cm by 30 cm:

What we know: length = 10 cm, width = 8 cm, height = 3 cm Volume = length × width × height = 10 × 8 × 3 = 240 cm³

(2) Calculate the volume of a cuboid that has dimensions 40 cm by 3 m by 70 cm:

First we must make all the measurements in the same units. Let’s convert 3 m to cm: 3 m = 300 cm Volume = length × width × height = 40 × 300 × 70 = 840,000 cm³

(3) What are the dimensions of a cuboid which has a volume of 4 m³ (cubic metres) and has a base area of 1 m² and what is the height:

Volume = base area × height = 1 × height = 4 Therefore, height = 4 m

(4) What is the volume of a cube with each side of 50 cm²?:

Volume = side³ = 50³ = 125,000 cm³

(5) A rectangular room has a width of 8m and length of 10m and the height is 3m. Calculate the volume:

Volume = length × width × height = 10 × 8 × 3 = 240 m³

(6) A cylinder has a radius of 10 cm and a height of 50cm and the capacity is 5m litres which the cylinder is 5m wide at the bottom and 10 cm wide at the top:

Volume = πr²h = 3.14 × 10² × 50 = 3.14 × 100 × 50 = 15,700 cm³

(7) A triangular prism has a base area of 40m² and height of 5 cm after the volume is 15m³:

Since area of base = 40 m² and height = 5 cm = 0.05 m Volume = base area × height = 40 × 0.05 = 2 m³

Volume and Capacity

Examples of Typical Cubic Units and Liquid Capacity:

1. Volume of liquid from glass bottle and cubic meter: 1 cubic meter = 1000 litres of liquid 1 litre = 1000 millilitres (ml) of liquid 
2. Capacity is also equal to measure on its: 1 cubic centimetre = 1 millilitre 1000 cubic metres = 1000 litres 1 litre = 1000 millilitres and hold 1000 cubic centimetres of water capacity 
3. A soap can be filled with water up to volume of 20 cm³. How much water can it hold? Since 1 cm³ = 1 mL Therefore 20 cm³ = 20 mL 
4. A container has volume of 2 litres. Its capacity is also 2 litres. How much water it can hold in millilitres? 2 litres = 2 × 1000 = 2000 mL 
5. If you can be the equal: We have lots many cylindrical in terms the amount of litres: 50 50ml of solution for every litre equal to amount of water. If 20 such solution litres, how many millilitres are equal in total? 20 litres = 20 × 1000 = 20,000 mL 
6. If we have one different units and we approximately consider the amount of water to: 1800 L of 50 mL water for equals. That is the amount of water for 1000 ml water equals in the amount of litres of 4.5 litres: How many 1800 L = 1800 × 1000 = 1,800,000 mL 
7. 300L to 100m litre: consider in cubic centimetre of 10 Litre = 300L of the volume of Cubic centimetre is at litres which equal to amount in the of litres = 5000 cm³ of How many = 5000 litres 300L = 300 × 1000 = 300,000 mL = 300,000 cm³ 
8. A plastic bottle has a capacity of litre. How many cubic centimetres it has the amount equal in the litres = 1 litre = 1000 cm³ 
9. An aluminum water bottle of 5 Litres, how many cubic centimetres it has quantity equal in 200ml = 5 litres = 5 × 1000 = 5000 cm³ 
10. A milk container has a volume of 4 litres, how many cubic centimetres it has the amount in ml into the litres it can hold = 4 litres = 4 × 1000 = 4000 cm³ = 4000 mL 
11. The formula for finding the volume of a cuboid is: Volume = length × width × height 
12. The formula for finding the volume of a cube is: Volume = side³ 
13. The formula for finding the volume of a triangular prism is: Volume = ½ × base × height × length 
14. The formula for finding the capacity (or volume) of a cylinder is: Volume = πr²h where π = 3.14, r = radius, h = height 
15. Conversions: 
    • 1 centimetre³ = _____ litres → 0.001 litres
    • 1 litre = _____ millilitres → 1000 millilitres
    • 1 cubic metre = _____ litres → 1000 litres

Objective Questions:

1. The volume of a cube measuring 5 litres dimensional sides of 5 sides = a) 25 cm³ b) 125 cm³ c) 75 cm³ d) 100 cm³ 
2. Which of the following is the capacity unit? a) cm³ b) Litre c) m³ d) kg 
3. 4 cm³ equals: a) 4 mL b) 4 L c) 400 mL d) 0.4 mL 
4. 5 Litres equals: a) 500 mL b) 50 mL c) 5000 mL d) 50000 mL 
5. A cube measures: a) Has 3 dimensions b) Has 2 dimensions c) Has 1 dimension d) Has no dimensions 
6. Volume is measured in: a) Litres b) Grams c) cubic units d) metres 
7. Capacity is measured in: a) cm³ b) Litres c) kg d) metres 
8. The volume of a cuboid having length 8cm, breadth 5cm, width = ________ cm³ a) 13 b) 18 c) 40 
9. The volume of a shape not including triangular, square unit = ________ volume a) 1 b) Cubic c) Litres d) cm³ 
10. 1 Litre equals: a) 100 mL b) 10 mL c) 1000 mL d) 10000 mL