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    This module and collection are included inLens: Siyavula: Mathematics (Gr. 7-9)
    By: Siyavula

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WISKUNDE

Omtrek, Oppervlakte en Volume

OPVOEDERS AFDELING

Memorandum

23.4

a) 108 kubieke cm

b) 72 kubieke cm

c) 23,625 kubieke cm

d) 108 kubieke cm

23.5

a) 20 kubieke cm

b) 63 000 kubieke mm

c) 24 000 kubieke cm

d) 1 728 kubieke cm

e) eie antwoord

LEERDERS AFDELING

Inhoud

AKTIWITEIT: Volume [LO 4.2, LO 4.3]

23. VOLUME

23.1 Het jy geweet?

Die hoeveelheid ruimte wat deur ’n vaste liggaam ingeneem word, word die volume van die liggaam genoem. Die volume is dus die ruimte binne ’n hol houer. Dit word ook die kapasiteit of inhoud van die houer genoem.

23.2 BELANGRIK om te ONTHOU!

Volume word in kubieke meeteenhede gemeet. Ons gebruik die volgende eenhede:

kubieke mm : mm³

kubieke cm : cm³

kubieke m : m³

1 cm³ (kubieke sentimeter) is ’n kubus met lengte, breedte en hoogte 1cm.

1 cm³ = 1 cm x 1 cm x 1 cm

= 10 mm x 10 mm x 10 mm

= 1 000 mm3

1 m³ = 1 m x 1 m x 1 m

= 100 cm x 100 cm x 100 cm

= 1 000 000 cm³

23.3 LEER ook die volgende:

Volume van ’n reghoekige prisma is lengte × breedte × hoogte

Volume van ’n kubus is y3(y = lengte, breedte en hoogte)

23.4 Gebruik die formule volume = lengte × breedte × hoogte Bereken die volume van die volgende figure:

Figure 1
Figure 1 (graphics1.png)
a)

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b)

Figure 2
Figure 2 (graphics2.png)

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c)

Figure 3
Figure 3 (graphics3.png)

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Figure 4
Figure 4 (graphics4.png)
d)

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23.5 a) Bereken die volume van die volgende in cm³

Figure 5
Figure 5 (graphics5.png)

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b) Bereken die volume van die volgende in mm³

Figure 6
Figure 6 (graphics6.png)

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c) Wat is die volume van die figuur in cm³?

Figure 7
Figure 7 (graphics7.png)

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d) Bereken die volume van ’n kubus met lengte 12 cm.

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e) Skat die volume van die krytdosie in jou klaskamer. .........................Meet nou die kante van die dosie en bereken die volume akkuraat.

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23.6 KLASBESPREKING

Hoe sal julle die volume van ’n onreëlmatige figuur, bv. ’n klip, bepaal?

23.6.1 Het jy geweet?

’n Griekse Wiskundige, Archimedes, het ontdek hoe om die volume van ’n onreëlmatige figuur te meet terwyl hy gebad het! Hy het gesien water spat oor die rand toe hy in die bad inklim. Hy het besef dat as hy die volume water wat sy liggaam verplaas, kan meet, kan hy bepaal wat die volume van sy eie liggaam is. Archimedes was so opgewonde dat hy uit die bad gespring en poedelnakend in die straat afgehardloop en “Eureka!” (Ek het dit gevind!) geskree het.

23.6.2 Volg die volgende stappe en kyk of jy die volume van ’n klippie wat jy buite kan optel, kan meet.

a) Vul ’n koppie heeltemal tot bo met water en sit dit in ’n groter houer (bak). Onthou om te kyk presies hoeveel ml water daar in jou koppie is.

b) Laat sak die klippie stadig in die koppie. Maak seker dat die water wat oorloop, in jou houer (bak) val.

c) Meet die hoeveelheid water in die bak met behulp van ’n maatbeker in mℓ.

d) Jou klippie het ’n volume van 1 cm³ vir elke mℓ water wat oorgeloop het, want 1 mℓ = 1 cm³.

e) Wat is die volume van jou klippie? .___________________________ ______

Assessering

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

Assesseringstandaard 4.2: Dit is duidelik wanneer die leerder probleme oplos;

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

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Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

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