Momwe mungawerengere Circumference wa bwalo ndendende?
Kuzungulira kwa bwalo ndi chidziwitso chofunikira cha masamu chomwe chimayambitsidwa kusukulu ya pulayimale kapena yapakati. Kudziwa kuzungulira kwa bwalo ndikofunikira kwa ophunzira omwe akukonzekera kuchita maphunziro apamwamba a masamu kusukulu yasekondale ndi koleji ndikukonzekera mayeso okhazikika monga SAT ndi ACT.
Mafunso a 10 Circumference of Circle Quiz omwe ali m'nkhaniyi adapangidwa kuti ayese kumvetsetsa kwanu pakupeza utali wa bwalo, m'mimba mwake, ndi mazungulira ake.
M'ndandanda wazopezekamo:
Kuzungulira kwa mkombero wa bwalo
Tisanayezedwe, tiyeni tibwereze mfundo zofunika kwambiri!
Kodi kuzungulira kwa bwalo ndi chiyani?
Kuzungulira kwa bwalo ndi mtunda wa mzere wa m'mphepete mwa bwalo. Ndilofanana ndi kuzungulira kwa mawonekedwe a geometric, ngakhale mawu akuti perimeter amangogwiritsidwa ntchito pa ma polygon.
Kodi mungapeze bwanji circumference wa bwalo?
Kuzungulira kwa fomula yozungulira ndi:
C = 2πr
kumene:
- C ndiye kuzungulira
- π (pi) ndi masamu osasinthasintha pafupifupi ofanana ndi 3.14159
- r ndi gawo lozungulira
Radiyo ndi mtunda kuchokera pakati pa bwalo kupita kumalo aliwonse m'mphepete.
The awiri ndi kawiri utali wozungulira, kotero circumference akhoza kuwonetsedwanso monga:
C = πd
kumene:
- d ndi m'mimba mwake
Mwachitsanzo, ngati utali wozungulira bwalo ndi 5 cm, ndiye circumference ndi:
C = 2πr = 2π * 5 cm = 10π cm
≈ 31.4 cm (kuzungulira mpaka 2 decimal)
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Kuzungulira kwa mafunso ozungulira
Funso 1: Ngati dziwe losambira lozungulira lozungulira ndi mamita 50, utali wake ndi wotani?
A. 7.95 mamita
B. 8.00 mamita
C. 15.91 mamita
D. 25 mamita
✅ Yankho Lolondola:
A. 7.95 mamita
Kufotokozera:
Ma radius angapezeke pokonzanso chilinganizo C = 2πr ndi kuthetsa r: r = C / (2π). Kulumikiza mozungulira mozungulira mita 50 ndikuyandikira π mpaka 3.14, timapeza kuti ma radius ndi pafupifupi 7.95 metres.
Funso 2: Kutalika kwa bwalo ndi mainchesi 14. Kodi radius yake ndi yotani?
A. 28 mainchesi
B.14 mainchesi
C. 21 mainchesi
D. 7 mainchesi
✅ Yankho Lolondola:
D. 7 mainchesi
Kufotokozera:
Popeza m'mimba mwake ndi kawiri utali wa utali wozungulira (d = 2r), mungapeze utali wozungulira pogawa m'mimba mwake ndi 2 (r = d / 2). Apa, kugawa m'mimba mwake wa mainchesi 14 ndi 2 kumabweretsa kutalika kwa 7 inchi.
Funso 3: Ndi ziganizo ziti mwa zotsatirazi zomwe ziri zoona ponena za mgwirizano wapakati ndi kuzungulira kwa bwalo?
A. M'mimba mwake ndi theka la circumference.
B. Kuzungulira kwake kumakhala kofanana ndi kuzungulira.
C. Kuzungulira kwake kuwirikiza kawiri.
D. M'mimba mwake ndi π kuchulukitsa kozungulira.
✅ Yankho Lolondola:
A. M'mimba mwake ndi theka la circumference.
Kufotokozera:
M'mimba mwake ndi wofanana ndi 2 nthawi ya radius, pamene circumference ndi yofanana ndi 2π nthawi ya radius. Choncho, m'mimba mwake ndi theka la circumference.
Funso 4: Gome lomwe tikuyenera kukhalapo lili ndi kuzungulira kwa mayadi 6.28. Tiyenera kupeza awiri a tebulo.
A.1 gawo
B. 2 mayadi
C. 3 mayadi
D. 4 mayadi
✅ Yankho Lolondola:
B. 2 mayadi
Kufotokozera:
Kuzungulira kwa bwalo kumawerengedwa pochulukitsa m'mimba mwake ndi pi (π). Pankhaniyi, circumference imaperekedwa ngati mayadi 6.28. Kuti tipeze m'mimba mwake, tifunika kugawa chigawocho ndi pi. Kugawa mayadi 6.28 ndi pi kumatipatsa pafupifupi mayadi awiri. Chifukwa chake, kutalika kwa tebulo ndi mayadi 2.
Funso 5: Munda wozungulira uli ndi 36 mita mozungulira. Kodi malo ozungulira dimbalo ndi otani?
A. 3.14 mamita
B. 6 mamita
C. 9 mamita
D. 18 mamita
✅ Yankho Lolondola:
C. 9 mamita
Kufotokozera:
Kuti mupeze utali wozungulira, gwiritsani ntchito njira yozungulira: C = 2πr. Konzaninso chilinganizo kuti muthetsere utali wozungulira: r = C / (2π). Mukalumikiza 36 metres mozungulira ndikugwiritsa ntchito pafupifupi π ngati 3.14, mumapeza r = 36 / (2 * 3.14) ≈ 9 mita.
Funso 6: Dziwe losambira lozungulira lili ndi utali wa mita 8. Kodi ndi mtunda wotani womwe wosambira amayenda mozungulira dziwe akamaliza mwendo umodzi?
A. 16 mamita
B. 25 mamita
C. 50 mamita
D. 100 mamita
✅ Yankho Lolondola:
C. 50 mamita
Kufotokozera:
Kuti mupeze mtunda womwe wosambira amayenda mozungulira dziwe pamlingo umodzi, mumagwiritsa ntchito njira yozungulira (C = 2πr). Pankhaniyi, ndi 2 * 3.14 * 8 mamita ≈ 50.24 mamita, yomwe ili pafupifupi 50 mamita.
Funso 7: Poyesa hula hoop m’kalasi, gulu C linapeza kuti linali ndi utali wa mainchesi 7. Kodi kuzungulira kwa hula hoop ndi chiyani?
A. 39.6 mainchesi
B. 37.6 mainchesi
C. 47.6 mainchesi
D. 49.6 mainchesi
✅ Yankho Lolondola:
C. 47.6 mainchesi
Kufotokozera:
Kuzungulira kwa bwalo kumatha kupezeka pogwiritsa ntchito njira C = 2πr, pomwe r ndi utali wozungulira wa bwalo. Pankhaniyi, radius ya hula hoop imaperekedwa ngati mainchesi 7. Kuyika mtengo uwu mu fomula, timapeza C = 2π(7) = 14π mainchesi. Poyerekeza ndi π mpaka 3.14, titha kuwerengera circumference ngati 14(3.14) = 43.96 mainchesi. Kuzunguliridwa ku chakhumi chapafupi, circumference ndi mainchesi 47.6, zomwe zimagwirizana ndi yankho lomwe laperekedwa.
Funso 8: Semicircle ili ndi radius ya 10 mita. Kodi perimeter yake ndi yotani?
A. 20 mamita
B. 15 mamita
C. 31.42 mamita
D. 62.84 mamita
✅ Yankho Lolondola:
C. 31.42 mamita
Kufotokozera: Kuti mupeze zozungulira za semicircle, werengani theka la kuzungulira kwa bwalo lonse ndi utali wa mita 10.
Funso 9: Gulu la basketball limasewera ndi mpira wokhala ndi mainchesi 5.6. Kodi basketball iliyonse imazungulira bwanji?
A. 11.2 mainchesi
B. 17.6 mainchesi
C. 22.4 mainchesi
D. 35.2 mainchesi
✅ Yankho Lolondola:
C. 22.4 mainchesi
Kufotokozera:
Mutha kugwiritsa ntchito njira yozungulira bwalo, yomwe ndi C = 2πr. Radiyo yopatsidwayo ndi mainchesi 5.6. Lumikizani mtengo uwu mu formula, tili ndi C = 2π * 5.6 mainchesi. C ≈ 2 * 3.14 * 5.6 mainchesi. C ≈ 11.2 * 5.6 mainchesi. C ≈ 22.4 mainchesi. Chifukwa chake, kuzungulira kwa basketball kulikonse kuli pafupifupi mainchesi 22.4. Izi zikuyimira mtunda wozungulira mpirawo.
Funso 10: Sarah ndi anzake awiri ankamanga tebulo lozungulira kuti asonkhane. Iwo ankadziwa kuti kuti onse akhale momasuka mozungulira tebulolo, ankafunika mtunda wa mamita 18 mozungulira. Kodi tebulo la pikiniki liyenera kukhala ndi mainchesi otani kuti lifike mozungulira?
A. 3 mapazi
B. 6 mapazi
C. 9 mapazi
D. 12 mapazi
✅ Yankho Lolondola:
B. 6 mapazi
Kufotokozera:
Kuti tipeze utali wozungulira, tagawani mozungulira ndi 2π, tili ndi r = C / (2π) r = 18 mapazi / (2 * 3.14) r ≈ 18 mapazi / 6.28 r ≈ 2.87 mapazi (ozungulira mpaka zana lapafupi).
Tsopano, kuti mupeze m'mimba mwake, ingowirikizani utali wozungulira: Diameter = 2 * Radius Diameter ≈ 2 * 2.87 feet Diameter ≈ 5.74 feet. Chifukwa chake, tebulo la picnic liyenera kukhala ndi mainchesi pafupifupi 5.74 mapazi
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Mafunso Ofunsidwa Kawirikawiri
2πr wa bwalo ndi chiyani?
2πr ndi njira yozungulira bwalo. Mu formula iyi:
- "2" ikuyimira kuti mukutenga kuwirikiza kwa utali wa radius. Kuzungulira kwake ndi mtunda wozungulira bwalo, kotero muyenera kuzungulira bwalo kamodzi kapena kawiri, chifukwa chake timachulukitsa ndi 2.
- “π” (pi) ndi masamu osasinthasintha pafupifupi ofanana ndi 3.14159. Amagwiritsidwa ntchito chifukwa amaimira mgwirizano pakati pa circumference ndi awiri a bwalo.
- "r" imayimira mtunda wa bwalo, womwe ndi mtunda kuchokera pakati pa bwalo kupita kumalo aliwonse ozungulira.
Chifukwa chiyani kuzungulira ndi 2πr?
Njira yozungulira bwalo, C = 2πr, imachokera ku tanthauzo la pi (π) ndi mawonekedwe a geometric a bwalo. Pi (π) amaimira chiŵerengero cha kuzungulira kwa bwalo kufika m'mimba mwake. Mukachulukitsa radius (r) ndi 2π, mumawerengera mtunda wozungulira bwalo, lomwe ndi tanthauzo la circumference.
Kodi chozungulira ndi kasanu ndi kawiri utali wozungulira?
Ayi, kuzungulira sikuli ndendende kuchulukitsa kwa 3.14 utali wozungulira. Ubale pakati pa circumference ndi utali wozungulira wa bwalo umaperekedwa ndi chilinganizo C = 2πr. Pomwe π (pi) ndi pafupifupi 3.14159, kuzungulira kwake ndi 2 kuwirikiza π kuchulukitsa kwa radius. Choncho, circumference ndi yoposa nthawi 3.14 ya radius; ndi 2 kuchulukitsa ndi π kuchulukitsa kwa utali.
Ref: Omni Caculator | Prof
