Hukama huripo pakati peArc Length neSector Area
Mumasvomhu, kunyanya mu plane geometry, kune pfungwa dzakakosha dzinosanganisira madenderedzwa. Pfungwa mbiri dzinowanzo kurukurwa ndedze arc length nenzvimbo ye sector. Kunzwisisa kwakanaka kwepfungwa idzi mbiri kunotibvumira kuverenga mativi akasiyana-siyana emadenderedzwa, kungave muzvidzidzo zvemasvomhu, mashandisirwo ehunyanzvi, kana hupenyu hwezuva nezuva.
Tsanangudzo yeDenderedzwa
Tisati taenderera mberi, zvinobatsira kunzwisisa kuti denderedzwa chii. Denderedzwa iboka remapoinzi ese ari mudenderedzwa ari chinhambwe chakatarwa kubva panzvimbo yakatarwa inonzi pakati. Daro iri rakatarwa rinozivikanwa se radius yedenderedzwa. Denderedzwa rine zvinhu zvakakosha zvakati wandei, zvinosanganisira:
1. Nzvimbo yepakati (O): Nzvimbo yakatarwa inoyerwa daro remamwe mapoinzi ese ari mudenderedzwa.
2. Radius (r): Daro kubva pakati penzvimbo kusvika chero panzvimbo iri mudenderedzwa.
3. Dhayamita (d): Daramita refu kubva pane imwe nzvimbo kuenda kune imwe padenderedzwa rinopfuura nepakati penzvimbo. Dhayamita yacho yakapetwa kaviri kureba kweradius.
4. Kutenderera (C): Kureba kwemutsetse wakakomberedza denderedzwa, kwakaverengwa uchishandisa fomura \( C = 2 \pi r \).
Kunzwisisa Kureba kweArc
Kureba kwearc ndiko kureba kwechikamu chakati chedenderedzwa redenderedzwa. Ngatifungidzirei denderedzwa guru rakachekwa nemitsara miviri ye radial. Mitsetse iyi ye radial inoparadzanisa denderedzwa kuita arcs mbiri, dzatinodaidza kuti ma major ne madiki, zvichienderana nekureba kwadzo.
Kuti tiverenge kureba kwe arc, tinofanira kuziva radius yedenderedzwa uye saizi ye central angle inoumbwa nemitsara miviri ye radial. Kureba kwe arc kunogona kuverengerwa uchishandisa fomura iyi:
\[ L = \theta \times r \]
di mana:
– \( L \) kureba kwe arc,
– \( \theta \) ndiyo kona yepakati muma radians,
– \( r \) ndiyo dhayamita yedenderedzwa.
Kana kona yepakati iri mumadhigirii, fomura inoshanduka kuita:
\[ L = \kuruboshwe( \frac{\theta}{360} \kurudyi) \kawa 2 \pi r \]
Semuenzaniso, kana uine denderedzwa rine radius yemayuniti gumi uye kona yepakati yemadhigirii makumi matanhatu, kureba kwe arc kunogona kuverengerwa seizvi:
\[ L = \kuruboshwe( \frac{60}{360} \kurudyi) \kanguva 2 \pi \kanguva 10 = \kuruboshwe( \frac{1}{6} \kurudyi) \kanguva 20 \pi = \frac{20 \pi}{6} \approx 10.47 \, \text{unit} \]
Tsanangudzo yeNzvimbo yeSector
Nzvimbo yechikamu inzvimbo yechikamu chakati chedenderedzwa chakaumbwa nemitsetse miviri yeradial uye arc inobatanidza. Mitsetse inowanzo fananidzwa nezvidimbu zvepai kana pizza. Kuti tiverenge nzvimbo yechikamu, tinoda radius yedenderedzwa uye kona yepakati yakaumbwa nemitsetse miviri yeradial.
Fomura yekuverenga nzvimbo yechikamu ndeiyi:
\[ A = \frac{1}{2} r^2 \theta \]
di mana:
– \( A \) inzvimbo yechikamu ichi,
– \( \theta \) ndiyo kona yepakati muma radians,
– \( r \) ndiyo dhayamita yedenderedzwa.
Kana kona yepakati iri mumadhigirii, fomura yacho inochinjwa kuita:
\[ A = \left( \frac{\theta}{360} \right) \times \pi r^2 \]
Semuenzaniso, ngatitii tine denderedzwa rine radius yemayuniti gumi uye kona yepakati yemadhigirii makumi matanhatu. Ipapo nzvimbo yechikamu inogona kuverengerwa seizvi:
\[ A = \kuruboshwe( \frac{60}{360} \kurudyi) \nguva \pi \nguva 10^2 = \kuruboshwe( \frac{1}{6} \kurudyi) \nguva 100 \pi = \frac{100 \pi}{6} \approx 52.36 \, \text{unit}^2 \]
Hukama Huri Pakati Pehurefu HweArc neSector Area
Pfungwa dzehurefu hwe arc nenzvimbo ye sector zvakabatana zvakanyanya nekuti zvese zvinoenderana ne radius yedenderedzwa ne central angle. Nekuziva chimwe chezviviri izvi neruzivo rwakawedzerwa senge radius kana central angle, tinogona kuverenga chimwe.
Hukama hwemasvomhu pakati pehurefu hwearc nenzvimbo yechikamu hunogona kuumbwa seizvi. Kubva pafomura yatinoziva kare:
1. Kureba kweArc: \[ L = \left( \frac{\theta}{360} \right) \times 2 \pi r \]
2. Nzvimbo yenet: \[ A = \left( \frac{\theta}{360} \right) \times \pi r^2 \]
Tinogona kuona kubva pamafomula maviri ari pamusoro apa kuti pane kufanana mu angular fraction \(\left( \frac{\theta}{360} \right)\) iyo inoratidza huwandu hwedenderedzwa rese rakaumbwa.
Kana tichida kubatanidza zviviri izvi mberi, cherechedza kuti kureba kwe arc \( L \) ipesenti yedenderedzwa redenderedzwa uye nzvimbo ye sector \( A \) ipesenti yenzvimbo yedenderedzwa. Nemamwe mashoko,
\[ L = \kuruboshwe( \frac{\theta}{360} \kurudyi) \kawa 2 \pi r \]
\[ A = \left( \frac{L}{2 \pi r} \right) \times \pi r^2 \]
Nyoresa zvikamu,
\[ A = \kuruboshwe( \frac{L}{2} \kurudyi) \nguva r \]
Saka tinogona kutaura zvakananga kuti, nzvimbo yechikamu inogona kuenderana nehurefu hwearc kuburikidza nehurefu hwearc uye radius:
\[ A = \frac{1}{2} L r \]
Mashandisirwo muHupenyu hweZuva Nezuva
Kunzwisisa hukama huripo pakati pehurefu hwearc nenzvimbo yechikamu hakusi kungodzidza chete, asiwo kune mashandisirwo anoshanda muzvikamu zvakasiyana-siyana zvehupenyu hwezuva nezuva. Mamwe emashandisirwo aya anosanganisira:
1. Kugadzira Magadzirirwo Ezvivakwa: Pakugadzira zvivakwa zvakaita semadomes, magadheni, kana zvivakwa zvakaita sedenderedzwa, kuverenga hurefu hwearc nenzvimbo yechikamu kwakakosha zvikuru.
2. Unyanzvi hweMichina: Mukugadzira zvikamu zvemuchina zvine mafambiro edenderedzwa kana edenderedzwa, ruzivo urwu runobatsira kuverenga nzira nenzvimbo zvinodiwa.
3. Kuongorora nyeredzi: Mukugadzira nzira dzekufamba kwemapuraneti kana masateraiti echisikigo akaita denderedzwa kana kuti akatenderera.
4. Kurima: Kunobatsira mukugadzira nzvimbo yekudiridza inotenderera pakati kuti mvura igoverwe zvakaenzana.
Mhedziso
Kunzwisisa hukama huripo pakati pehurefu hwe arc nenzvimbo ye sector kunotibvumira kunzwisisa zviri nani kuti makona, radii, nezvimwe zvikamu zvedenderedzwa zvinodyidzana sei. Nekushandisa maformula aya ekutanga, tinogona kugadzirisa matambudziko akasiyana-siyana mumasvomhu e geometric pamwe nekushandiswa kunoshanda munzvimbo dzakasiyana-siyana, kusanganisira kuvaka, mainjiniya, kurima, uye nyeredzi. Pfungwa idzi mbiri, kunyange dzichiita sedziri nyore, dzine mashandisirwo akapararira muhupenyu hwezuva nezuva, zvichiita kuti dzive dzakakosha kudzidza nekuziva.
