Om die struktuur van sommige regte prismas te verstaan
[LU 3.3, 3.4]
A.
Bou houers
Daar sal aan jou ‘n vel papier met vorms gegee word. Jy benodig ‘n liniaal waarmee jy kan meet, ‘n skêr en gom of kleefband. Kleurpotlode sal ook help. Doen die volgende:
Meet al die lyne en skryf jou mate netjies neer (jy behoort tot die naaste half-millimeter te kan meet). Doen ook jou bes om die deursnee (of die radius) van die sirkel te meet. As jy ‘n gradeboog beskikbaar het, bepaal ook waar die 90° hoeke is.
Bepaal nou die oppervlaktes van al die vorms vanuit jou mates. Tel die verskillend dele bymekaar om die totale oppervlaktes van die vier verskillende vorms te bereken. Sit jou werk versigtig uiteen sodat enigeen kan begryp wat jy doen. Gebruik die regte name vir die vorms waarmee jy werk.
Byvoorbeeld, vir die laaste figuur sou dit so lyk:
Totale oppervlakte = klein reghoek + klein reghoek + groot reghoek
= (l × b) + (l × b) + (l × b)
ensovoorts . . . (Onthou om altyd geskikte eenhede te gebruik.)
Sny nou die vorms versigtig uit. Jy kan hulle inkleur as dit jou sou help om die bokant en onderkant van die sykante (met die strepe) te onderskei. Vou die vorms nou en gebruik kleefband of gom en papierstrokies om vier houertjies te maak. Hou die kante met die strepe aan die buitekant.
Skryf die
Totale Buite-Oppervlakte (TBO) van elke vorm neer. (Dis wat jy reeds bereken het!)
Werk saam in groepies van drie of vier en probeer uitwerk hoeveel 1cm × 1cm blokkies in elk van die houers sou inpas. Hierdie waarde is
volume van die houer. As julle ‘n metode of formule kan vind wat vir elkeen van die vorms sou werk, skryf dit sorgvuldig neer.
As jy klaar is met hierdie oefening behoort jy twee formules te hê.
B.
Regte prismas
Hierdie vier houers is elk ‘n
regte prisma . Hierdie vorms het ‘n basis en ‘n bokant wat presies dieselfde grootte en vorm het, met sye wat reguit boontoe loop en ‘n 90° hoek vorm met die basis. Soek vir jou items wat aan hierdie vereistes voldoen en dus regte prismas is.
Ons benoem regte prismas volgens die vorm van die basis, byvoorbeeld vierkantige prisma, reghoekige prisma, driehoekige prisma en sirkelvormige prisma (silinder).
Is hierdie twee vorms regte prismas? Beskryf die vorm van elkeen se basis en bevestig of die sye regop loop teen 90° met die basis.
C.
Formules
Om die totale buite-oppervlakte (TBO) en volume (V) van enige regte prisma te bereken, gebruik ons die volgende algemene formules: (Let op dat H na die prisma se hoogte verwys.)
TBO = 2 × basisoppervlakte + sy-oppervlakte en V = basisoppervlakte × prismahoogte
Die volgende voorbeelde is belangrik. Dit is die vier houers wat jy uitgesny en gevou het. Let op dat elke afdeling van die berekening apart gedoen word en dan uiteindelik in die formule ingestel word.
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