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Wiskunde

Omtrek, oppervlakte en volume

Opvoeders afdeling

Memorandum

Suiker / rys / sand maak kubus vol

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 liters

MODULE TOETS

1.

a) 4

b) 30 000

c) 6

d) 2,5

e) 5

f) 2 000 000

g) 1

h) 1 000

2.

a) kubus

b) piramide

  • 8
  • 5

4.

5. 114 mm

6. 48,72 kubieke cm

7. Braaikamer= 28,125 vierkante meter

Teëls = 0,0625 vierkante meter

Teëls benodig: 45

8.

a) Tenk hou 38,985 kubieke meter = 38 985 000 kubieke cm

Dus: 38 985 liters

b) 38,985 kl

Leerders afdeling

Inhoud

Aktiwiteit: volume en inhoud [lu 4.3, lu 4.5]

24. VOLUME EN INHOUD

24.1 Kom ons kyk na die twee terme: volume en inhoud .

VOLUME

Hoeveelheid ruimte deur iets ingeneem.

Word in kubieke eenhede gemeet: m³; cm³; mm³

INHOUD

Verwys gewoonlik na vloeistowwe.

Word gewoonlik in kℓ, liter of mℓ gemeet

24.2 LET OP:

Jy weet reeds 1 cm³ = 1 mℓKom ons kyk nou hoeveel cm ³ is daar in 1 liter

  • Teken die volgende ontvouing op karton (wees akkuraat!)

§ Knip dit dan uit en vou al op die stippellyne.

§ As jy reg gewerk het, sal jy ’n kubus hê van 1 000 cm ³ .

§ Neem nou enige liter bottel of maatsilinder wat 1 liter kan hou en maak dit vol suiker, rys of sand. Gooi dit oor in jou kubus. Wat merk jy op?

  • Voltooi: 1 liter = __________________ mℓ

= _________________________ cm³

24.3 Vul die ontbrekende antwoorde in:

a) 500 mℓ = __________________ cm³

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

c) 30 mℓ = __________________ cm³

d) __________________ mℓ = 1 500 cm³ = __________________ liter

e) 3 liter = __________________ cm³

f) __________________ liter = 950 cm³

24.4 Die binnemate van ’n bad is 60 cm by 140 cm by 35 cm. Hoeveel liter water sal in die bad wees as dit halfvol is?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

25. Tyd vir selfassessering

  • Maak ’n regmerkie in die toepaslike kolom:
Ja Nee
Ek kan die volgende begrippe verduidelik:
  • Inhoud
  • Volume
Ek weet in watter eenhede volume gemeet word
Ek kan cm ³ na mm ³ herlei en andersom
Ek kan m ³ na cm ³ herlei en andersom
Ek ken die formule vir die volume van ’n
  • Reghoekige prisma
  • Kubus
Ek kan die volume van figure korrek bereken
Ek weet hoe om die volume van ’n onreëlmatige figuur te bepaal
Ek kan ml na cm ³ herlei en andersom
Ek kan liter na cm 3 herlei en andersom

26. UITDAGING!

’n Maatskappy wat lekkers bemark, vra jou om ’n houer te ontwerp vir ’n nuwe soort lekker. Elke lekker lyk soos ’n gelyksydige drie­hoek waarvan die sye 3 cm lank is. Elke lekker is 1 cm dik.

a) Ontwerp die houer! Besluit self hoeveel van die bogenoemde lekkers in jou houer sal kan pas.

b) Ontwerp ’n etiket vir die houer wat die aandag van moontlike kopers sal trek!

Assessering

Leeruitkomste 4: Die leerder is in staat om gepaste meeteenhede, instrumente en formules in ‘n verskeidenheid kontekste te gebruik.

Assesseringstandaard 4.3: Dit is duidelik wanneer die leerder probleme oplos deur ‘n verskeidenheid strategieë te gebruik;

Assesseringstandaard 4.5: Dit is duidelik wanneer die leerder die volgende bereken deur die geskikte formules te gebruik.

Module toets

1. Vul die ontbrekende antwoord in.

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. Wat noem ons die volgende figure?

a)

_______________________________________

b)

_______________________________________

(2)

3.1 Hoeveel hoekpunte het figuur a? _____________________________

3.2 Hoeveel syvlakke het figuur b? ________________________________

(2)

4. Twee dele van die ontvouing van die figuur ontbreek. Trek hulle in.

(2)

5. Bereken die omtrek van die volgende figuur:

(3)

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

(3)

6. Bereken die oppervlakte van ’n reghoek in cm 2 met lengte 87 mm en breedte 56 mm.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

(3)

7. My braaikamer is 6,25 m lank en 4,5 m breed. Ek wil die vloer bedek met teëls van 250 mm by 250 mm. Hoeveel teëls benodig ek?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

(5)

8. Die binnemate van ’n reghoekige vistenk is 3 m by 2,3 m by 5,65 m.

a) Hoeveel liter water kan hierdie vistenk hou?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

(4)

b) Hoeveel kiloliter water kan die vistenk hou?

_____________________________________________________________________

(1)

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Source:  OpenStax, Wiskunde graad 7. OpenStax CNX. Oct 21, 2009 Download for free at http://cnx.org/content/col11076/1.2
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