4.8 Volume and capacity

Mathematics

Perimeter, area and volume

Educator section

Memorandum

sugar / rice / sand fills up cube

1 000

1 000

24.3

a) 500

b) 200; 200

c) 30

d) 1 500; 1,500

e) 3 000

f) 0,950

147 litres

MODULE TEST 8

1.

a) 4

b) 30 000

c) 6

d) 2,5

e) 5

f) 2 000 000

g) 1

h) 1 000

2.

a) cube

b) pyramid

• 8
• 5

4.

5. 114 mm

6. 48,72 cubic cm

7. Braai room = 28,125 square metres

Tiles = 0,0625 square metres

Tiles needed: 45

8.

a) Tank holds 38,985 cubic metres = 38 985 000 cubic cm

Therefore: 38 985 litres

b) 38,985 kl

Leaner section

Content

Activity: volume and capacity [lo 4.3, lo 4.5]

24. VOLUME AND CAPACITY

24.1 Let us look at the two terms : volume and capacity :

VOLUME

How much space something occupies.Is measured in cubic units: m³; cm³; mm³

CAPACITY

Normally refers to liquids.Normally measured in kℓ, litre or mℓ

24.2 NOTE:

You know already that 1 cm³ = 1 mℓ

Let us see how many cm³ are in 1 ℓ

• Draw the following net on cardboard. (Be accurate.)

§ Now cut it out and fold along all the dotted lines..

§ If you have worked correctly, you will have a cube of 1 000 cm3.

§ Now take any 1 ℓ bottle or measuring cylinder and fill it with sugar, rice or sand. Empty it into your cube. What do you see?

• Complete: 1 litre = __________________ mℓ

= _________________________ cm³

24.3 Fill in the missing answers

a) 500 mℓ = __________________ cm³

b) __________________ mℓ = 0,200 litre = __________________ cm³

c) 30 mℓ = __________________ cm³

d) __________________ mℓ = 1 500 cm³ = __________________ litre

e) 3 litre = __________________ cm³

f) __________________ litre = 950 cm³

24.4 The inside measurements of a bath are 60 cm by 140 cm. by 35 cm.

How many litres of water does the bath take when it is half-full?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

25. Time for self-assessment

26. CHALLENGE!

A sweet company asks you to design a container for a new type of sweet. Each sweet looks like an equilateral triangle that has sides 3 cm long. Each sweet is 1 cm thick.

a) Design the container. Decide how many of these sweets will fit into your container.

b) Design a label for the container that will attract the attention of potential customers!

Assessment

Learning Outcome 4: The learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts.

Assessment Standard 4.3: We know this when the learner solves problems using a range of strategies;

Assessment Standard 4.5: We know this when the learner calculates, by selecting and using appropriate formulae.

Module test

1. Fill in the missing answer:

a) 400 mm² = __________________ cm²

b) 3 m² = __________________ cm²

c) 6 000 000 m² = __________________ km²

d) 20 500 m² = __________________ ha

e) 5 000 mm³ = __________________ cm³

f) 2 m³ = __________________ cm³

g) 1 cm³ = __________________ ml

h) 1 litre = __________________ cm³ (8 x 1 = 8)

2. What do we call the following figures?

_______________________________________

_______________________________________

(2)

3.1 How many vertexes does figure A have? _____________________________

3.2 How many faces does figure B have? ________________________________

(2)

4. Two sections of the net are missing. Draw them in.

(2)

5. Calculate the perimeter of the following figure:

(3)

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

(3)

6. Calculate the area of a rectangle in cm2. Its length is 87 mm and breadth is 56 mm.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

(3)

7. My entertainment area is 6,25 m by 4,5 m. I want to tile the floor with tiles of 250 mm by 250 mm. How many tiles do I need?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

(5)

8. The inside measurements of a rectangular fish tank are 3 m by 2,3 m by 5,65 m.

a) What is the capacity, in litres, of the fish tank?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

(4)

b) What is its capacity in kilolitres?

_____________________________________________________________________

(1)