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Volume en buite-oppervlakte van regte prismas

Module by: Siyavula Uploaders. E-mail the author

WISKUNDE

Grade 8

VERHOUDINGS EN EWEREDIGHEID

METING EN VORMLEER

KONSTRUKSIES

Module 16

VOLUME EN BUITE-OPPERVLAKTE VAN REGTE PRISMAS

AKTIWITEIT 1

Om die volume en die buite-oppervlakte van regte prismas te ontdek en ‘n formule vir die berekening daarvan te formuleer, en die toepassing van die ontdekte formules in praktiese situasies te gebruik [LU 3.8, 4.2, 4.3, 4.5]

  • Inligting wat van nut kan wees in die uitvoer van hierdie ondersoek moet hier neergeskryf word. Jou onderwyser sal jou help om seker te maak dat die inligting korrek is, voordat jy met die ondersoek begin.

1. Skryf die formules vir die berekening van die oppervlakte en volume van elk van die volgende figure neer:

1.1 Oppervlakte van ‘n vierkant:

1.2 Oppervlakte van ‘n reghoek:

1.3 Oppervlakte van ‘n driehoek:

1.4 Oppervlakte van ‘n sirkel:

1.5 Volume van ‘n reghoekige prisma:

1.6 Volume van ‘n silinder:

2. Beskryf wat jy onder elk van die volgende verstaan en maak ‘n skets daarvan.

2.1 reghoekige prisma:

2.2 driehoekig prisma:

2.3 kubus:

2.4 silinder:

3. Wat verstaan jy onder die woord “volume”?

4. In watter standaardeenhede word die volgende gemeet?

  • volume:
  • water in ‘n dam, koeldrank in ‘n bottel:

5. Bestudeer die volgende voorstellings van nette.

5.1 reghoekige prisma:

Figure 1
Figure 1 (graphics1.png)

5.2 driehoekige prisma (dit is nie ‘n regte piramide nie):

Figure 2
Figure 2 (Picture 3.png)

Assessering

Table 1
LU 3
Ruimte en VormDie leerder is in staat om eienskappe van en verwantskappe tussen twee- dimensionele vorms en drie-dimensionele voorwerpe in ’n verskeidenheid oriënta-sies en posisies te beskryf en voor te stel.
Assesseringstandaarde(ASe)
 
3.3 gebruik woordeskat om parallelle lyne te beskryf wat deur ’n dwarslyn, loodlyne en snylyne gekruis word, asook driehoeke na aanleiding van hoekverwantskappe (bv. vertikaal teenoorstaande, ooreenkomstig);3.4 gebruik ’n passer, liniaal en gradeboog om meetkundige figure akkuraat te konstrueer sodat spesifieke eienskappe ondersoek en nette ontwerp kan word;3.5 ontwerp en gebruik nette om modelle te maak van meetkundige driedimensionele voorwerpe wat tot en met hierdie graad bestudeer is;3.7 gebruik proporsie om die uitwerking van vergroting en verkleining op die eienskappe van meetkundige figure te beskryf;3.8 teken en interpreteer sketse van meetkundige driedimensionele voorwerpe vanuit verskillende perspektiewe, met aandag aan die behoud van eienskappe.
LU 4
MetingDie leerder is in staat om gepaste meeteenhede, -instrumente en formules in ’n verskeidenheid kontekste te gebruik.
Dit is duidelik wanneer die leerder:
4.1 los ingewikkelder probleme op wat tyd behels, insluitend die verhouding tussen tyd, afstand en spoed;4.2 los probleme op wat die volgende behels:4.2.1 lengte;4.2.2 omtrek en oppervlakte van veelhoeke en sirkels;4.2.3 en volume en buite-oppervlakte van reghoekige prismas silinders.
4.3 los probleme op deur ’n verskeidenheid strategieë te gebruik, insluitend:4.3.1 skatting;4.3.2 berekening tot minstens twee desimale plekke;4.3.3 die gebruik en omskakeling van toepaslike SI eenhede;
4.5 bereken die volgende deur die geskikte formulas te gebruik:4.5.1 omtrek van veelhoeke en sirkels;4.5.2 oppervlakte van driehoeke, reghoeke, sirkels en veelhoeke deur ontbinding tot driehoeke en reghoeke;4.5.3 volume van prismas met driehoekige en reghoekige basisse en silinders.
4.7 skat, vergelyk, meet en teken hoeke met ’n gradeboog, akkuraat tot een graad.

Memorandum

AKTIWITEIT 1

  • 2
  • ℓ × b
  • 1212 size 12{ { {1} over {2} } } {} × b × size 12{ ortho } {}h
  • π π size 12{π} {} r 2
  • ℓ × b × h
  • π π size 12{π} {} r 2 h

2. Leerders voorsien.

3. Inhoud

  • ℓ / mℓ / kℓ / cm3 / mm3 ens.
  • kℓ / ℓ / mℓ

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