Ukubala Umthamo Wesilinda
Isilinda singenye yezimo zejiyometri ezivame kakhulu esihlangana nazo ekuphileni kwansuku zonke. Ukuma kwaso kulula: sinezisekelo ezimbili eziyindilinga kanye nesivalo, esinehlangothi eligobile elizihlanganisayo. Izinto eziningi ezisizungezile ziyindilinga, njengezibuko, amathini okuphuza, amadramu amanzi, amapayipi, ngisho namasilinda egesi. Ngenxa yokutholakala kwazo, ukuqonda ukuthi ungabala kanjani ivolumu yesilinda kuyikhono eliyisisekelo eliwusizo, kokubili ezifundweni zezibalo kanye nangezinjongo ezisebenzayo njengokulinganisa umthamo wezitsha.
Iyini ivolumu yesilinda?
Umthamo wesilinda uyisilinganiso sesikhala esinezilinganiso ezintathu esingasibamba. Ngamanye amazwi, umthamo ubonisa ukuthi isilinda singasibamba okuqukethwe okungakanani, njengamanzi, isihlabathi, noma umoya. Amayunithi asetshenziselwa umthamo ngokuvamile amayunithi e-cubic, njenge-cm³, m³, noma amalitha (qaphela: ilitha eli-1 = 1000 cm³).
Ukuze sibone ngeso lengqondo ivolumu yesilinda, singacabanga ngendilinga njengesisekelo, bese indilinga "ibekwa" ekuphakameni okuthile. Uma isisekelo sikhulu (i-radius yendilinga inkulu), ivolumu yesilinda inkulu. Uma isilinda side, ivolumu iba nkulu.
Izinto ze-Tube okudingeka uzazi
Ngaphambi kokubala ivolumu , sidinga ukuqonda izinto eziningana ezibalulekile zesilinda:
1. Irediyasi (r)
Irediyasi ibanga elisuka enkabeni yendilinga eyisisekelo kuya emaphethelweni endilinga. Irediyasi ivame ukukhonjiswa ngohlamvu u-r.
2. Ububanzi (d)
Ububanzi buyibanga elisuka kolunye uhlangothi lwesiyingi liye kolunye phakathi nendawo. Ubudlelwano bayo nerediyasi buyi:
d = 2r noma r = d/2 .
3. Ukuphakama (t)
Ukuphakama ibanga eliphakathi kwesisekelo kanye nengxenye ephezulu yesilinda. Ukuphakama kwesilinda kuvame ukukhonjiswa ngu-t.
4. π (pi)
I-π iyi-constant yezibalo enenani elicishe libe ngu-3,14 noma 22/7. Inani le-π lisetshenziswa ku- ukubalwa kwendilinga.
Ifomula yevolumu yesilinda
Ifomula yevolumu yesilinda ivela emqondweni olula: ivolumu yesilinda ilingana nendawo yesisekelo ephindaphinda ukuphakama.
Indawo yesisekelo sesilinda yi indawo yendilinga, leyo:
Indawo yendilinga = πr²
Ngakho-ke ifomula yevolumu yesilinda yile:
V = πr²t
Imininingwane:
– V = ivolumu yesilinda
– π = 3,14 noma 22/7
– r = irediyasi yesisekelo
– t = ukuphakama kwesilinda
Le fomula ibaluleke kakhulu ngoba cishe yonke imibuzo mayelana nomthamo wesilinda izogcina isebenzisa le fomula.
Izinyathelo zokubala ivolumu yesilinda
Ukuze ugweme amaphutha, landela lezi zinyathelo:
1. Qiniseka ukuthi uyazi irediyasi noma ububanzi
– Uma wazi ububanzi, qala ngokubuguqula bube yi-radius ngokubuhlukanisa ngo-2.
2. Qiniseka ukuthi amayunithi ayafana
– Uma i-radius iku-cm, ukuphakama kumele futhi kube ku-cm.
– Uma irediyasi ingamamitha, ukuphakama kumele futhi kube ngamamitha.
3. Sebenzisa ifomula V = πr²t
4. Bala ngokucophelela
– Yenza irediyasi ibe yi-square (r²).
– Phindaphinda ngo-π.
– Phindaphinda umphumela ngokuphakama (t).
5. Bhala imiphumela ngamayunithi evolumu (amayunithi e-cubic)
Isibonelo sokubala ivolumu yesilinda
Isibonelo 1: Uma sibheka irediyasi nokuphakama
Isilinda sinobubanzi obungu-7 cm kanye nokuphakama okungu-10 cm. Bala ivolumu.
Isixazululo:
V = πr²t
V = (22/7) × 7² × 10
V = (22/7) × 49 × 10
V = 22 × 7 × 10
V = 1540 cm³
Ngakho-ke ivolumu yesilinda ingu-1540 cm³.
Isibonelo 2: Ububanzi nokuphakama okwaziwayo
Ithini eliyindilinga linobubanzi obungu-14 cm kanye nokuphakama okungu-20 cm. Lingakanani ivolumu yalo?
Isinyathelo sokuqala: thola irediyasi
r = d/2 = 14/2 = 7 cm
Isixazululo:
V = πr²t
V = (22/7) × 7² × 20
V = 22 × 7 × 20
V = 3080 cm³
Ngakho-ke umthamo wethini ungama-3080 cm³.
Isibonelo 3: Ukusebenzisa i-π = 3,14
Isilinda sinobubanzi obungu-5 cm kanye nokuphakama okungu-12 cm. Bala ivolumu yaso.
Isixazululo:
V = 3,14 × 5² × 12
V = 3,14 × 25 × 12
V = 3,14 × 300
V = 942 cm³
Ngakho-ke ivolumu ingu-942 cm³.
Guqula ivolumu yesilinda ibe amalitha
Empilweni yansuku zonke, sivame ukufuna ukwazi amandla esilinda ngamalitha, isibonelo amandla ebhodlela lamanzi noma isigubhu.
Ngicela uqaphele:
– ilitha eli-1 = 1000 cm³
– 1 m³ = amalitha ayi-1000
Isibonelo, uma ivolumu yesilinda ingu-3080 cm³, khona-ke ngamalitha:
3080 ÷ 1000 = 3,08 amalitha
Lokhu kwenza kube lula ngathi ukuqonda amandla ngamagama ajwayelekile.
Amaphutha avamile
Ngisho noma ifomula ilula, amaphutha alandelayo avame ukwenziwa:
1. Ngikhohliwe ukuguqula ububanzi bube yirediyasi
Abafundi abaningi bafaka ngokushesha ububanzi kufomula ye-r², noma ngabe kufanele basebenzise irediyasi.
2. Iyunithi engalungile
Isibonelo, uma u-r eku-cm kodwa u-t eku-mitha, umphumela awunangqondo. Amayunithi kumele afane.
3. Ngikhohliwe ukukala irediyasi
Ifomula ingu-r², hhayi u-r. Ngakho-ke u-r kumele aphindwe ngo-r.
4. Ukukhetha okungalungile kwenani le-π
Sebenzisa u-22/7 uma u-r eyi-multiple ka-7 ukuze kube lula. Ngaphandle kwalokho, sebenzisa u-3,14.
Ukusetshenziswa kwevolumu yesilinda empilweni
Ukubala ivolumu yesilinda akusizi nje kuphela ezinkingeni zezibalo, kodwa futhi nasezidingweni ezahlukahlukene zomhlaba wangempela, njenge:
– Bala umthamo wethangi lamanzi eliyindilinga.
– Ukulinganisa umthamo wamapayipi okugcina noma amasilinda.
– Nquma inani lezinto ezidingekayo esitsheni esiyisilinda (isib. inhlama, upende, noma usimende).
– Linganisa umthamo wethini noma ibhodlela lomkhiqizo.
Ngokuqonda imiqondo namafomula, singenza izibalo ezinembile nezisebenzayo.
Isiphetho
Umthamo wesilinda uyisilinganiso sokuthi isilinda singabamba isikhala esingakanani. Ukuze siwubale, sidinga nje ukwazi irediyasi yesisekelo (noma ububanzi, obube sebuguqulwa bube yirediyasi) kanye nokuphakama kwesilinda. Ifomula eyisisekelo ithi:
V = πr²t
Ngokulandela izinyathelo ezifanele, ukugcina amayunithi ahambisanayo, kanye nokucophelela lapho sibala, singanquma kalula umthamo wesilinda. Leli khono lizoba usizo kokubili ezibalweni nasezimweni zansuku zonke, ikakhulukazi lapho sidinga ukulinganisa umthamo wesitsha noma into esilinda.
Uma uthanda, ngingenza nemibuzo yokuzijwayeza ngezingxoxo noma inguqulo elula yesihloko sezinga lesikole samabanga aphansi/esikoleni esiphakathi.
