Ububanzi besangqa ngumlinganiselo osisiseko osivumela ukuba siqonde iimpawu kunye neempawu zalo mfanekiso wejometri. Kweli nqaku, siya kuphonononga ngobuchule inkqubo yokumisela ububanzi besangqa. Ukususela kwizinto ezisisiseko ukuya kwiifomyula zemathematika eziyimfuneko, siya kunika isikhokelo esipheleleyo nesichanekileyo ekubaleni lo mlinganiselo ubalulekileyo. Ukuba unomdla wokuqonda ngokupheleleyo ububanzi besangqa kwaye uyisebenzise kwiingxaki zakho zemathematika kunye nokuzivocavoca, awukwazi ukuphosakela eli nqaku. Masingene kwiinkcukacha!
1. Inkcazo kunye neengcamango ezisisiseko zobubanzi besangqa
Ubukhulu besangqa ngumlinganiselo esetyenzisiweyo ukumisela owona mgama mkhulu phakathi kwamanqaku amabini achaseneyo kwisangqa sesangqa. Ukuze uqonde ngcono le ngcamango, kubalulekile ukukhumbula ukuba ububanzi buhlala buphindwe kabini kwi-radius yesangqa.
Ukubala ubukhulu besangqa, ungasebenzisa ifomula yemathematika d = 2r, apho 'd' imele idayamitha kwaye 'r' imele iradiyasi. Kubalulekile ukuqaphela ukuba zombini i-diameter kunye ne-radius yesangqa zilinganiswa kwiiyunithi ezifanayo zobude, nokuba iisentimitha, iimitha, i-intshi, phakathi kwabanye.
Indlela elula yokujonga ububanzi kukudweba umgca ochanekileyo odlula phakathi kwesangqa kwaye uphele nakweyiphi na indawo kwi-circumference. Lo mgca othe tye umele ububanzi besangqa. Ngokwazi ububanzi besangqa, sinokuyisebenzisa ukubala ezinye iimpawu zesangqa, ezifana nomjikelezo, indawo kunye nobude be-arc.
2. Ifomula yokubala ubukhulu besangqa
Ukubala ububanzi besangqa ngumsebenzi olula kakhulu. Ubukhulu besangqa buchazwa ngokuphindwe kabini ubude beradiyasi yaso. Ukufumana i-diameter, siphinda-phinda ixabiso leradiyasi ngo-2. Apha ngezantsi kukho ingcaciso ecacileyo yendlela yokubala ububanzi besangqa.
Inyathelo lesi-1: Chonga ixabiso leradiyasi yesangqa. Iradiyasi ngumgama olinganiswa ukusuka kumbindi wesangqa ukuya kuyo nayiphi na indawo kwisangqa sayo. Qinisekisa ukuba ixabiso leradiyasi likwiyunithi enye ofuna ukuyisebenzisela umlinganiselo.
Inyathelo lesi-2: Ukusebenzisa ifomula yedayamitha, phinda-phinda ixabiso leradiyasi ngo-2. Oko kukuthi, ububanzi = 2 * irediyasi. Sebenzisa ixabiso leradiyasi elichongiweyo kwiNyathelo loku-1 kwaye wenze uphindaphindo oluhambelanayo. Lo msebenzi uya kukunika ixabiso elichanekileyo lobubanzi besangqa.
Iingcebiso:
- Khumbula ukuba i-diameter isoloko inkulu kune-radius.
- Sebenzisa izixhobo zokubala okanye izixhobo ze-intanethi ukuba ufuna iziphumo ezichanekileyo okanye ukuba ufuna ukubala ububanzi besangqa kunye ne-radius engaziwayo.
3. Amanyathelo okumisela ububanzi besangqa
Ukumisela ububanzi besangqa, kuyimfuneko ukulandela amanyathelo amaninzi aya kusivumela ukuba sisombulule ingxaki. Ngezantsi, siza kuchaza ngalinye kula manyathelo ngokweenkcukacha:
Inyathelo lesi-1: Chonga ulwazi olukhoyo noluyimfuneko. Ngaphambi kokuqala ukusombulula ingxaki, kubalulekile ukwazi idatha esinayo kunye nedatha esifuna ukuyifumana. Kule meko, kufuneka sazi i-perimeter okanye i-circumference yesangqa.
Inyathelo lesi-2: Sebenzisa ifomyula efanelekileyo yemathematika. Ububanzi besangqa buhambelana ngokuthe ngqo kwi-circumference okanye i-perimeter. Ifomula enxulumanisa le milinganiselo mibini yile: d = C/πapho d imele ubukhulu, C imele isangqa kunye π isoloko iqikelelwa kwi-3.1415.
Inyathelo lesi-3: Faka endaweni yamaxabiso aziwayo kwifomula kwaye wenze izibalo eziyimfuneko. Sakuba sinefomula echanekileyo, sibeka ngokulula endaweni yexabiso lesangqa kwinxaki kwaye senze imisebenzi yeemathematika eyimfuneko ukufumana ixabiso ledayamitha.
4. Ukusebenzisa isangqa ukufumana ubukhulu besangqa
Emva koko, siya kuchaza indlela yokusebenzisa i-circumference yesangqa ukuze sifumane ububanzi baso. Ukuqala, kubalulekile ukukhumbula ukuba i-circumference yesangqa ichazwa njengomgama ojikeleze umda wayo. Ngoko ke, inyathelo lokuqala lokufumana ububanzi kukulinganisa ubude bomjikelezo.
Emva kokuba ubude besangqa bufunyenwe, ifomyula yemathematika ingasetyenziselwa ukubala ububanzi. Ifomula yile ilandelayo: Idayamitha = isangqa / π. Apho u-π eyinto engatshintshiyo emalunga ne-3.14159. Yahlula ngokulula ubude bomjikelezo ngo π kwaye isiphumo esifunyenweyo siya kuba lixabiso ledayamitha.
Ngokomzekelo, masithi silinganise umjikelezo wesangqa kwaye sifumene ixabiso le-31.42 cm. Ukusebenzisa ifomyula, sinokubala ububanzi ngolu hlobo lulandelayo: ububanzi = 31.42 cm / π ≈ 9.99 cm. Ngoko ke, ubukhulu obusondeleyo besangqa yi-9.99 cm.
5. Ukusebenzisa ulungelelwaniso lwesangqa ukufumana ubukhulu
Ukufumana i-diameter yesangqa usebenzisa izilungelelanisi zaso, kufuneka silandele amanyathelo amaninzi. Okokuqala, kubalulekile ukukhumbula ukuba ububanzi besangqa bulingana neradius ephindwe kabini. Ke ngoko, ukuba siyazazi ulungelelwaniso lombindi wesangqa kunye nolungelelwaniso lwalo naliphi na inqaku elikwisangqa, sinokumisela iradiyasi size sifumane i-diameter ngokuphindaphinda iradiyasi ngamabini.
Ukubala i-radius, sinokusebenzisa ifomula yomgama phakathi kwamanqaku amabini kwinqwelomoya yeCartesian. Siya kukwazi ulungelelwaniso lombindi wesangqa (x1, y1) kunye nolungelelwaniso lwalo naliphi na iphuzu kwisangqa (x2, y2), kwaye sinokusebenzisa ifomula:
irediyasi = sqrt((x2 – x1)^2 + (y2 – y1)^2)
Sakuba sineradiyasi, sinokufumana i-diameter ngokuphinda-phinda iradiyasi ngesibini. Ngokomzekelo, ukuba i-radius i-5 units, ngoko ububanzi besangqa buya kuba yiyunithi ezili-10.
6. Iindlela ezizezinye zokubala ububanzi besangqa
Ukubala ububanzi besangqa ngumsebenzi oqhelekileyo kwimathematika kunye nejometri. Ukongeza kwindlela eqhelekileyo, kukho iindlela ezininzi ezizezinye ezinokusetyenziswa ukufumana iziphumo ezichanekileyo. ngokufanelekileyo. Apha zintathu iindlela ezizezinye ezinokusetyenziswa:
- Ifomula yobubanzi: Eyona ndlela isisiseko yokubala i-diameter yesangqa kukusebenzisa ifomula yemathematika d = 2r, apho "d" imele ububanzi kunye no "r" yiradius. Le fomula ilula kwaye ithe ngqo, iyenza ilungele ukubala ngokukhawuleza. Umzekelo, ukuba uyayazi iradiyasi yesangqa, uphinda-phinda ngo-2 ukufumana idiameter.
- Umlinganiselo othe ngqo: Enye indlela yokubala ububanzi besangqa kukulinganisa ngokuthe ngqo usebenzisa irula, umlinganiselo weteyiphu, okanye esinye isixhobo sokulinganisa. Isixhobo sibekwe kumgca othe ngqo kumbindi wesangqa kwaye umlinganiselo uthathwa ukusuka kwelinye iphuzu kwisangqa ukuya kwelinye elichaseneyo. Olu buchule luluncedo ngakumbi xa usebenza ngezinto ezibonakalayo.
- Iindlela zeJometri: Kwakhona kunokwenzeka ukumisela ububanzi besangqa usebenzisa ezinye iindlela zejometri. Umzekelo, unokuzoba umgca we-tangency ukuya kwisangqa nakweyiphi na indawo kwaye emva koko ulinganise umgama ngokwe-perpendicularly ukusuka kwindawo ye-tangency ukuya kwidayamitha echaseneyo. Kukho izixhobo ze-intanethi kunye nesoftware ekhethekileyo enokunceda kwezi ntlobo zokubala.
7. Imizekelo esebenzayo yendlela yokufumana ububanzi besangqa
Kule nqaku, siza kuhlolisisa imizekelo ebonakalayo yendlela yokubala ububanzi besangqa. Okulandelayo, siza kuveza iindlela ezintathu ezilula eziza kukunceda ukusombulula le ngxaki ngempumelelo.
Indlela yoku-1: Ukusebenzisa ifomula yedayamitha. Ifomula yokubala ububanzi besangqa ngokulula kabini iradiyasi (D = 2r). Ukuba unexabiso leradiyasi, phinda-phinda elo xabiso ngo-2 ukufumana idiameter. Ngokomzekelo, ukuba i-radius yesangqa yi-5 cm, ububanzi buya kuba yi-10 cm.
Indlela yesi-2: Ukulinganisa ngerula okanye iteyiphu yokulinganisa. Ukuba unesangqa somzimba ofuna ukubala ububanzi baso, ungasebenzisa irula okanye umlinganiselo weteyiphu ukulinganisa iradiyasi. Beka irula okanye i-tape yokulinganisa phezu kombindi wesangqa kwaye unwebe kumda, uqinisekise ukuba umlawuli u-perpendicular ukuya kumda wesangqa. Ixabiso olifumanayo liya kuba yidayamitha yesangqa.
Indlela yesi-3: Ukusebenzisa isixhobo se-intanethi. Ukuba ukhetha ukungenzi izibalo zezandla, ungasebenzisa isixhobo se-intanethi ukubala ububanzi besangqa. Kukho iinketho ezininzi ezikhoyo, kwaye ngokuqhelekileyo uya kufuna kuphela ukungena kwi-radius ixabiso kwaye ucofe "Bala" ukufumana i-diameter. Ezi zixhobo ziluncedo ngakumbi xa usebenza kunye nezangqa ezinkulu okanye ukuba ufuna ukwenza izibalo ngokukhawuleza.
Khumbula ukuba ubukhulu besangqa ngumlinganiselo osisiseko onokusetyenziswa kwiimeko ezahlukeneyo, ukusuka kwiingxaki zemathematika ukuya kusetyenziso olusebenzayo kwiinkalo ezahlukeneyo. Le mizekelo isebenzayo ikunika iindlela ezahlukeneyo zokubala ububanzi, kwaye unokukhetha eyona ndlela ifanele iimfuno zakho kunye nezinto ozikhethayo. Siyathemba ukuba olu lwazi luluncedo kuwe ekusombululeni iingxaki zakho ngokubala ububanzi besangqa!
8. Izixhobo eziluncedo ukubala ububanzi besangqa
Ukubala ububanzi besangqa, kukho izixhobo ezininzi eziluncedo ezikhoyo ezenza inkqubo ibe lula. Ngezantsi zezinye zazo:
1. Ifomula yemathematika: Ububanzi besangqa bungabalwa kusetyenziswa i-formula D = 2r, apho i-D imele ububanzi kunye no-r yi-radius. Kufuneka nje ukwazi ixabiso leradiyasi ukuze ukwazi ukubala i-diameter.
- Umzekelo: Ukuba iradiyasi yesangqa yi-5 cm, ngoko ke ububanzi buya kuba yi-2 * 5 cm = 10 cm.
2. Izicelo ze-intanethi: Kukho izixhobo ze-intanethi ezikuvumela ukuba ubale ububanzi besangqa kumcimbi wemizuzwana. Ezi zicelo zicela ixabiso leradiyasi njengegalelo kwaye zibuyisela iziphumo zokubala ngokuzenzekelayo.
- Ingcebiso: Xa usebenzisa ezi zixhobo, kubalulekile ukuqinisekisa ukuba iyunithi yokulinganisa esetyenziselwa i-radius iyafana njengoko kulindelwe ngenxa yobubanzi.
3. Isoftware yokuyila imizobo: Iinkqubo ezininzi zoyilo lwegraphic, ezifana nePhotoshop okanye Illustrator, nazo zinezixhobo ezikuvumela ukuba uzobe kwaye usebenzise imizobo yejometri, kuquka izangqa. Ezi nkqubo zihlala zibonelela ngemisebenzi ukubala ngokuzenzekelayo ububanzi besangqa ukusuka kwiradiyasi.
- Ingcebiso: Ukuba usebenzisa isoftwe yoyilo lwegraphic, luluvo oluhle ukuphonononga iinketho ezikhoyo kunye nesetingi ukuqinisekisa ukuba usebenzisa umsebenzi ochanekileyo kwaye ufumana iziphumo ezichanekileyo.
9. Iingqwalasela kunye nezilumkiso xa ulinganisa ububanzi besangqa
Xa ulinganisa ububanzi besangqa, kubalulekile ukugcina iingqwalasela kunye nezilumkiso engqondweni ukuze ufumane iziphumo ezichanekileyo. Ngezantsi ngamanyathelo athile kunye nezindululo ekufuneka zilandelwe ukwenza lo mlinganiselo ngokuchanekileyo:
1. Sebenzisa i-caliper okanye isixhobo esifanelekileyo sokulinganisa ukufumana iziphumo ezichanekileyo. Oku kuya kuqinisekisa ukuba umlinganiselo wenziwa ngokuchanekileyo nangokungaguquguqukiyo.
2. Qinisekisa ukuba umbindi wesangqa uchongiwe ngokucacileyo phambi kokulinganisa ububanzi bawo. Oku Inokufezekiswa ngokusebenzisa ubuchule bokucwangcisa nokumakisha, obufana nokusebenzisa ikhampasi okanye irula, ukufumana indawo esembindini.
3. Beka isixhobo sokulinganisa i-perpendicular kububanzi besangqa. Oku kuthetha ukuba isixhobo kufuneka sibe kwi-angle echanekileyo kwi-axis yesangqa, esiya kunceda ukuqinisekisa umlinganiselo ochanekileyo.
10. Ukubaluleka kwedayamitha kwijometri kunye nezinye iinkalo
Idayamitha ngumlinganiselo osisiseko kwijometri, osetyenziswa ukuchaza nokuchaza iimilo zejiyometri kunye nemifanekiso eyahlukeneyo. Kwijometri ye-Euclidean, idiameter ngowona mlinganiselo umde onokufunyanwa phakathi kwamanqaku amabini kumfanekiso, udlula embindini wawo. Lo mlinganiso ubaluleke kakhulu kwisifundo sezangqa kunye neengqungquthela, kuba ububanzi bunquma ubungakanani kunye neempawu zabo.
Kwamanye amacandelo anjengefiziksi kunye nobunjineli, idiameter nayo idlala indima ebalulekileyo. Ngokomzekelo, xa uyila izakhiwo okanye amacandelo omatshini, i-diameter isetyenziselwa ukugqiba imilinganiselo kunye nokulungelelaniswa okufanelekileyo phakathi kwamalungu. Oku kubaluleke ngakumbi kwiimeko apho kufuneka ukudibanisa okuchanekileyo, okufana neebheringi okanye iigiya. Ukongeza, i-diameter iphinda isetyenziswe ukubala iindawo, imiqulu kunye nobunye ubungakanani bomzimba.
Kubalulekile ukuqaphela ukuba i-diameter ayisebenzi kuphela kwizinto ezintathu-dimensional, kodwa nakwiimilo ezisicaba, ezifana neepolygons kunye ne-ellipses. Umzekelo, kwipolygon eqhelekileyo, i-diameter ngumgca odlula embindini kwaye i-perpendicular to amacala amabini izichasi. Ukwazi eli xabiso kunokuba luncedo kwizibalo zejometri okanye ukufumana ii-symmetries ezongezelelweyo kunye neempawu zomfanekiso. Isishwankathelo, ukufundwa kwedayamitha kubalulekile kwijometri nakwamanye amacandelo, njengoko kusivumela ukuba siqonde ngcono iimpawu kunye neempawu zeemilo ezahlukeneyo kunye nezakhiwo.
11. Ubudlelwane phakathi kwedayimitha kunye nezinye iimpawu zesangqa
Ububanzi besangqa ngumlinganiselo osisiseko ochaphazela ngokuthe ngqo ezinye iimpawu ezibalulekileyo zomfanekiso wejometri. Ukwazi ubudlelwane phakathi kobubanzi kunye nezi zakhiwo kubalulekile ukuqonda ngcono iimpawu zesangqa kwaye wenze izibalo ezichanekileyo.
Enye yezona zinto zichaphazelekayo ezihambelana nobubanzi bubude bomjikelezo. Ifomula yokubala ubude besangqa sesangqa C = πdapho C imele isangqa kunye d yidamitha. Olu ngqamaniso lubonisa ngokucacileyo ukuba ububanzi buyinto ephambili emisela ubude bomjikelezo.
Enye ipropati ebalulekileyo exhomekeke kububanzi yindawo yesangqa. Ummandla wesangqa ubalwa kusetyenziswa ifomula A = πr^2apho A yindawo kwaye r Yiradiyasi. Nangona kunjalo, iradiyasi inxulumene ngokuthe ngqo nobubanzi, kuba iradiyasi isisiqingatha sobubanzi (r = d/2). Ke ngoko, sinokugqiba ukuba ububanzi bukwachaphazela indawo yesangqa.
12. Ububanzi besangqa kumxholo wosetyenziso olusebenzayo
Idayamitha yesangqa ngumlinganiselo osisiseko kwijometri kwaye ineendlela ezahlukeneyo zokusebenza ezisebenzayo kwimimandla efana nobunjineli, ifiziksi. kunye noyilo lwezakhiwo. Kule nqaku, siza kuhlolisisa indlela yokubala ububanzi besangqa kunye nendlela esetyenziswa ngayo kwiimeko zangempela.
Ukubala ububanzi besangqa, kufuneka kuqala sazi ixabiso leradiyasi. Iradiyasi ngumgama ukusuka kumbindi wesangqa ukuya kuyo nayiphi na indawo kwisangqa sayo. Sakuba sineradiyasi, sinokusebenzisa ifomula yodayamitha esixelela ukuba ububanzi bulingana neradiyasi kabini (D = 2R).
Umzekelo wokusetyenziswa okusebenzayo kobubanzi besangqa kukwakhiwa kwamavili. Xa usenza amatayara, kubalulekile ukwazi ububanzi ukuze uqiniseke ukuba zilingana iirim zakho ngokufanelekileyo. Ukongezelela, kuyilo lwesekethe ye-elektroniki, ububanzi bezangqa bumele ubungakanani bamacandelo kwaye busetyenziselwa ukubala umgama phakathi kwabo. Ukwazi ukubala nokuqonda ububanzi besangqa kusivumela sombulula iingxaki ezisebenzayo kwezi nkalo kunye nezinye ezininzi.
13. Ukuzivocavoca kunye neengxaki zokuziqhelanisa nokubala ubukhulu besangqa
Ukuziqhelanisa ukubala ububanzi besangqa, kufuneka uqale uqonde iziseko. Ububanzi besangqa ngumgca othe tye ohamba embindini wesangqa kwaye udibanisa amanqaku amabini kumda. Ubude bayo buphindwe kabini iradiyasi yesangqa. I-radius, inxalenye yayo, ngumgama phakathi kombindi wesangqa kunye nayiphi na indawo ekumda wayo.
Enye indlela yokubala i-diameter kukusebenzisa ifomyula yemathematika D = 2r, apho u-D emele ububanzi kunye ne-r iradiyasi yesangqa. Ukwenza oku, kufuneka wazi ixabiso le-radius kwaye uphindaphinde ngo-2. Ukuba ixabiso le-radius alaziwa, kodwa unexabiso lendawo okanye umjikelezo wesangqa, ezinye iifomyula zingasetyenziswa.
Ukubala ububanzi ukusuka kwindawo yesangqa, ungasebenzisa ifomula D = √(4A/π), apho i-D iyi-diameter kunye no-A yindawo yesangqa. Kuyimfuneko ukwazi ixabiso lendawo kwaye usebenzise imathematika engaguqukiyo π (pi) malunga ne-3.14159. Enye indlela yokubala ububanzi ukusuka kwisangqa sesangqa kukusebenzisa ifomula D = C/π, apho u-D ngububanzi kunye no-C kwisangqa sesangqa. Kule meko, kuyimfuneko ukwazi ixabiso le-circumference kwaye usebenzise ixabiso lika-π.
14. Izigqibo zendlela yokufumana ububanzi besangqa
Isishwankathelo, bala ububanzi besangqa Yinkqubo ilula noko. Okokuqala, kufuneka sikhumbule ukuba ububanzi buphinda kabini umlinganiselo weradiyasi yesangqa. Ngoko ke, ukuba siyayazi iradiyasi, siphinda-phinda ixabiso layo ngesibini. Ukuba ingxaki isinika iperimeter okanye indawo yesangqa, sinokusebenzisa iifomyula ezithile ukufumana ububanzi.
Indlela eqhelekileyo esetyenziswayo yifomula yomjikelezo, echaza ukuba iperimeter yesangqa ilingana namaxesha amabini u-pi (π) ophindwe ngeradiyasi. Ekubeni i-diameter iphinda kabini iradiyasi, sinokufumana ifomula yokufumana i-dayamitha kwifomula yomjikelezo, sahlule iperimeter ngo-pi (π) ukufumana i-diameter.
Ngokukwanjalo, ukuba siyayazi indawo yesangqa, sinokusebenzisa ifomyula yendawo ukumisela iradiyasi kwaye siyiphindaphinde kabini ukufumana ububanzi. Ifomula yendawo ithi indawo yesangqa ilingana no-pi (π) ophindwe ngeradiyasi ephindwe kabini. Emva kokufumana iradiyasi, siphinda-phinda kabini ukufumana i-diameter efunekayo.
Isishwankathelo, ukubala ubukhulu besangqa kubalulekile ukuqonda ijometri yayo kunye nokwenza izibalo ezichanekileyo kwizicelo ezahlukeneyo zobugcisa nezesayensi. Kulo lonke eli nqaku, sihlolisise iindlela ezahlukeneyo zokumisela ububanzi besangqa, ukusuka kumlinganiselo othe ngqo kunye nokusetyenziswa kweefomyula ezisisiseko zemathematika, ukusetyenziswa kwezixhobo eziphambili ezifana ne-calipers kunye nesofthiwe ekhethekileyo. Ukuthathela ingqalelo ukuchaneka okufanelekileyo kunye nendlela yokusebenza kubalulekile ukufumana iziphumo ezithembekileyo nezichanekileyo. Siyathemba ukuba eli nqaku linikeze ulwazi oluyimfuneko ukuze uqonde ngokuchanekileyo kwaye usebenzise iikhonsepthi ezinxulumene nobubanzi besangqa kwiimeko ezahlukeneyo zobugcisa. Ngalo lonke ixesha ukhumbule ukudibana nemithombo ethembekileyo kwaye uguqukele kwiingcali ukuba unemibuzo okanye ujongene nemingeni enzima ngakumbi kulo mmandla. Ngolwazi olulungileyo kunye nokuziqhelanisa, uya kukwazi ukuqonda ubungakanani besangqa kwaye uthathe ithuba lokunceda iiprojekthi zakho kunye nezifundo zobugcisa.
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