Volume and Capacity – Basic 6 Mathematics Lesson Note (Third Term)

What is Volume?

Volume is the amount of space inside a 3D shape. We measure volume in cubic units like cm³, m³.

What is Capacity?

Capacity is how much liquid a container can hold. We measure capacity in litres (l) and millilitres (ml).

Remember: 1 litre = 1000ml

Volume of Different Shapes

Cube

A cube has all sides equal. 

Formula: Volume = length × length × length = l³

Cuboid

A cuboid has length, width and height. 

Formula: Volume = length × width × height

Cylinder

A cylinder is round with flat top and bottom. 

Formula: Volume = πr²h (where π = 22/7, r = radius, h = height)

Cone

A cone has a circular base and pointed top. 

Formula: Volume = ⅓πr²h

EXERCISES

1. Find the volume of these cubes:

1. Side = 4cm. Volume = _______
2. Side = 5m. Volume = _______
3. Side = 3cm. Volume = _______

1. Find the volume of these cuboids:

1. Length = 6cm, Width = 4cm, Height = 3cm. Volume = _______
2. Length = 8m, Width = 5m, Height = 2m. Volume = _______
3. Length = 10cm, Width = 6cm, Height = 4cm. Volume = _______

1. Convert these capacities:

1. 3 litres = _______ ml
2. 2500ml = _______ litres
3. 5.5 litres = _______ ml

1. Find the volume of cylinders: (Use π = 22/7)

1. Radius = 7cm, Height = 10cm. Volume = _______
2. Radius = 3.5cm, Height = 8cm. Volume = _______

1. Real Life Problems:

1. A water tank is 2m long, 1.5m wide and 1m high. How much water can it hold?
2. Funmi has a cylindrical bucket with radius 14cm and height 20cm. What is its volume?
3. A juice carton is 8cm long, 6cm wide and 12cm high. How much juice does it contain?

1. Quantitative Reasoning:

1. Which container holds more water?
   1. Container A: 4cm × 5cm × 6cm
   2. Container B: 3cm × 8cm × 5cm
2. A cube has volume 64cm³. What is the length of each side?
3. If a cylindrical tank holds 1540cm³ of water and has radius 7cm, what is its height? (Use π = 22/7)

1. Word Problems:

1. Kola wants to fill a rectangular swimming pool that is 10m long, 6m wide and 2m deep. How many litres of water does he need?
2. A cylindrical water drum has diameter 28cm and height 50cm. How much water can it store in litres?
3. Compare the volumes: A cube with side 6cm vs a cuboid 8cm × 4cm × 5cm. Which is bigger?

Answers: 

A: 1.64cm³ 2.125m³ 3.27cm³ 

B: 1.72cm³ 2.80m³ 3.240cm³ 

C: 1.3000ml 2.2.5litres 3.5500ml 

D: 1.1540cm³ 2.308cm³ 

E: 1.3m³ 2.12320cm³ 3.576cm³ 

F: 1.Container B(120cm³ vs 100cm³) 2.4cm 3.10cm 

G: 1.120000litres 2.30.8litres 3.Cube(216cm³ vs 160cm³)