Kuwerengera Voliyumu ya Silinda
Silinda ndi imodzi mwa mawonekedwe odziwika bwino omwe timakumana nawo tsiku ndi tsiku. Mawonekedwe ake ndi osavuta: ali ndi maziko awiri ozungulira ndi chivindikiro, chokhala ndi mbali yokhota yolumikiza. Zinthu zambiri zotizungulira ndi zozungulira, monga magalasi, zitini za zakumwa, migolo yamadzi, mapaipi, komanso masilinda a gasi. Chifukwa cha kupezeka kwawo konsekonse, kumvetsetsa momwe mungawerengere kuchuluka kwa silinda ndi luso lofunikira, pamaphunziro a masamu komanso pazinthu zothandiza monga kuyerekeza kuchuluka kwa ziwiya.
Kodi voliyumu ya silinda ndi yotani?
Kuchuluka kwa silinda ndi muyeso wa malo atatu omwe ingasunge. Mwanjira ina, kuchuluka kumasonyeza kuchuluka kwa zinthu zomwe silindayo ingasunge, monga madzi, mchenga, kapena mpweya. Mayunitsi omwe amagwiritsidwa ntchito pa kuchuluka kwa zinthu nthawi zambiri amakhala mayunitsi a cubic, monga cm³, m³, kapena malita (dziwani: lita imodzi = 1000 cm³).
Kuti tiwone kukula kwa silinda, tikhoza kuganiza za bwalo ngati maziko, kenako bwalo "limayikidwa" kutalika kwinakwake. Pamene maziko ali akulu (radius ya bwalo ili yaikulu), ndiye kuti voliyumu ya silinda imakhala yayikulu. Pamene silinda ili yayitali, voliyumu imakulanso.
Zinthu za chubu zomwe muyenera kudziwa
Tisanawerengere kuchuluka kwa voliyumu, tiyenera kumvetsetsa zinthu zofunika kwambiri za silinda:
1. Utali wozungulira (r)
Chizunguliro ndi mtunda wochokera pakati pa bwalo loyambira mpaka m'mphepete mwa bwalo. Chizunguliro nthawi zambiri chimawonetsedwa ndi chilembo r.
2. M'mimba mwake (d)
Dayamita ndi mtunda wochokera mbali imodzi ya bwalo kupita ku ina kudzera pakati. Ubale wake ndi radius ndi:
d = 2r kapena r = d/2 .
3. Kutalika (t)
Kutalika ndi mtunda pakati pa maziko ndi pamwamba pa silinda. Kutalika kwa silinda nthawi zambiri kumawonetsedwa ndi t.
4. π (pi)
π ndi chiwerengero cha masamu chomwe mtengo wake uli pafupifupi 3,14 kapena 22/7. Mtengo wa π umagwiritsidwa ntchito powerengera kuzungulira kwa bwalo.
Fomula ya voliyumu ya silinda
Fomula ya voliyumu ya silinda imachokera ku lingaliro losavuta: voliyumu ya silinda ndi yofanana ndi dera la maziko nthawi ndi kutalika.
Dera la maziko a silinda ndi dera la bwalo, lomwe ndi:
Malo ozungulira = πr²
Kotero njira ya voliyumu ya silinda ndi iyi:
V = πr²t
Zambiri:
– V = voliyumu ya silinda
– π = 3,14 kapena 22/7
– r = utali wa maziko
– t = kutalika kwa silinda
Fomula iyi ndi yofunika kwambiri chifukwa pafupifupi mafunso onse okhudza kuchuluka kwa silinda amatha kugwiritsa ntchito fomula iyi.
Masitepe owerengera kuchuluka kwa silinda
Kuti mupewe zolakwika, tsatirani izi:
1. Onetsetsani kuti mukudziwa radius kapena diameter
- Ngati mukudziwa kukula kwake, choyamba musinthe kukhala radius pogawa ndi 2.
2. Onetsetsani kuti mayunitsiwo ndi ofanana
– Ngati utali wa radius uli mu cm, kutalika kuyeneranso kukhala mu cm.
- Ngati radius ili mu mamita, kutalika kuyeneranso kukhala mu mamita.
3. Gwiritsani ntchito fomula V = πr²t
4. Werengani mosamala
– Ikani sikweya pa radius (r²).
– Chulukitsani ndi π.
- Chulukitsani zotsatira ndi kutalika (t).
5. Lembani zotsatira zake mu mayunitsi a voliyumu (mayunitsi a kiyubiki)
Chitsanzo cha kuwerengera voliyumu ya silinda
Chitsanzo 1: Poganizira za utali ndi kutalika
Silinda ili ndi utali wa masentimita 7 ndi kutalika kwa masentimita 10. Werengani kuchuluka kwake.
Yankho:
V = πr²t
V = (22/7) × 7² × 10
V = (22/7) × 49 × 10
V = 22 × 7 × 10
V = 1540 cm³
Kotero voliyumu ya silinda ndi 1540 cm³.
Chitsanzo 2: M'mimba mwake ndi kutalika kodziwika
Chidebe chozungulira chimakhala ndi mainchesi 14 m'mimba mwake ndi kutalika kwa masentimita 20. Kodi kukula kwake ndi kotani?
Gawo loyamba: pezani radius
r = d/2 = 14/2 = 7 cm
Yankho:
V = πr²t
V = (22/7) × 7² × 20
V = 22 × 7 × 20
V = 3080 cm³
Kotero voliyumu ya chidebecho ndi 3080 cm³.
Chitsanzo 3: Kugwiritsa ntchito π = 3,14
Silinda ili ndi utali wa masentimita 5 ndi kutalika kwa masentimita 12. Werengani kuchuluka kwake.
Yankho:
V = 3,14 × 5² × 12
V = 3,14 × 25 × 12
V = 3,14 × 300
V = 942 cm³
Kotero voliyumu yake ndi 942 cm³.
Sinthani voliyumu ya silinda kukhala malita
Mu moyo watsiku ndi tsiku, nthawi zambiri timafuna kudziwa mphamvu ya silinda mu malita, mwachitsanzo mphamvu ya botolo la madzi kapena ng'oma.
Chonde dziwani:
– lita imodzi = 1000 cm³
– 1 m³ = malita 1000
Mwachitsanzo, ngati voliyumu ya silinda ndi 3080 cm³, ndiye kuti mu malita:
3080 ÷ 1000 = malita 3,08
Izi zimapangitsa kuti zikhale zosavuta kuti timvetse mphamvu m'mawu odziwika bwino.
Zolakwa zofala
Ngakhale kuti njira imeneyi ndi yosavuta, zolakwika zotsatirazi nthawi zambiri zimachitika:
1. Ndayiwala kusintha dayamita kukhala radius
Ophunzira ambiri nthawi yomweyo amalowa m'mimba mwake mu fomula ya r², ngakhale ayenera kugwiritsa ntchito radius.
2. Chigawo cholakwika
Mwachitsanzo, ngati r ali mu cm koma t ali mu mamita, zotsatira zake sizomveka. Mayunitsi ayenera kukhala ofanana.
3. Ndayiwala kuyika sikweya yozungulira
Fomula ndi r², osati r. Choncho r iyenera kuchulukitsidwa ndi r.
4. Kusankha molakwika mtengo wa π
Gwiritsani ntchito 22/7 ngati r ndi multiple ya 7 kuti zikhale zosavuta. Apo ayi, gwiritsani ntchito 3,14.
Kugwiritsa ntchito voliyumu ya silinda pa moyo
Kuwerengera voliyumu ya silinda sikuti ndi kothandiza pa mavuto a masamu okha, komanso pa zosowa zosiyanasiyana zenizeni, monga:
- Werengani kuchuluka kwa thanki yamadzi yozungulira.
- Kuwerengera kuchuluka kwa mapaipi kapena masilinda osungiramo zinthu.
- Dziwani kuchuluka kwa zinthu zomwe zikufunika mu chidebe chozungulira (monga mtanda, utoto, kapena simenti).
- Yesani kuchuluka kwa chidebe kapena botolo la chinthucho.
Mwa kumvetsetsa mfundo ndi njira zake, titha kupanga mawerengedwe olondola komanso ogwira mtima.
Mapeto
Kuchuluka kwa silinda ndi muyeso wa malo omwe silinda ingathe kusunga. Kuti tiwerenge, timangofunika kudziwa utali wa maziko (kapena dayamita, womwe umasinthidwa kukhala utali wa radius) ndi kutalika kwa silinda. Fomula yoyambira ndi iyi:
V = πr²t
Mwa kutsatira njira zoyenera, kusunga mayunitsi ofanana, komanso kukhala osamala powerengera, titha kudziwa mosavuta kuchuluka kwa silinda. Luso limeneli lidzakhala lothandiza pa masamu komanso pazochitika za tsiku ndi tsiku, makamaka pamene tikufunika kuyerekeza mphamvu ya chidebe kapena chinthu chozungulira.
Ngati mukufuna, ndithanso kuyankha mafunso oyeserera ndi zokambirana kapena nkhani yosavuta ya sukulu ya pulayimale/yapakati.
