Yadda za a lissafta Da'irar daidai?
Kewayar da'irar wani ilimin lissafi ne na asali da ake buƙata wanda aka gabatar a makarantar firamare ko ta tsakiya. Kwarewar kewaya da'irar yana da mahimmanci ga ɗaliban da suka shirya yin ƙarin darussan lissafi a makarantar sakandare da koleji kuma suka shirya don daidaitattun jarrabawa kamar SAT da ACT.
An tsara Da'irar Tambayoyi 10 na Da'irar a cikin wannan labarin don gwada fahimtar ku na gano radius, diamita, da kewayen da'irar.
Table of Contents:
Da'irar dabarar da'irar
Kafin yin gwaji, bari mu sake tattara wasu mahimman bayanai!
Menene kewayen da'ira?
Da'irar da'irar ita ce tazarar madaidaiciyar gefen da'irar. Yana daidai da kewayen siffa na geometric, kodayake kalmar kewaye ana amfani da ita kawai don polygons.
Yadda ake nemo kewayen da'ira?
Kewayar dabarar da'ira ita ce:
C = 2πr
inda:
- C shine kewaye
- π (pi) mathematics akai-akai kusan 3.14159
- r shine radius na da'irar
Radius shine nisa daga tsakiyar da'irar zuwa kowane wuri a gefen.
Diamita ya ninka radius, don haka za a iya bayyana kewaye kamar haka:
C = πd
inda:
- d shine diamita
Alal misali, idan radius na da'irar ya kasance 5 cm, to, kewaye shine:
C = 2πr = 2π * 5 cm = 10π cm
≈ 31.4 cm (zagaye zuwa wurare 2 na decimal)
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Da'irar tambayoyin da'irar
Tambaya ta 1: Idan kewayen wurin wankan da'ira ya kai mita 50, menene radius?
A. 7.95 mita
B. 8.00 mita
C. 15.91 mita
D. 25m
✅ Amsa Daidai:
A. 7.95 mita
Ƙarin bayani:
Ana iya samun radius ta hanyar sake tsara dabara C = 2πr da warwarewa don r: r = C / (2π). Toshe kewayen da aka bayar na mita 50 da kusan π zuwa 3.14, mun sami radius kusan mita 7.95.
Tambaya 2: Diamita na da'irar shine inci 14. Menene radiyonsa?
A. 28 inci
B.14 inci
C. 21 inci
D.7 inci
✅ Amsa Daidai:
D.7 inci
Ƙarin bayani:
Tun da diamita ya ninka tsawon radius (d = 2r), za ku iya samun radius ta hanyar rarraba diamita ta 2 (r = d / 2). radius na 14 inci.
Tambaya ta 3: Wanne daga cikin waɗannan maganganun wanne ne gaskiya game da alakar da ke tsakanin diamita da kewayen da'ira?
A. Diamita shine rabin kewaye.
B. Diamita daidai yake da kewaye.
C. Diamita ya ninka dawafi.
D. Diamita shine π sau dawafi.
✅ Amsa Daidai:
A. Diamita shine rabin kewaye.
Ƙarin bayani:
Diamita yayi daidai da radius sau 2, yayin da kewaye yayi daidai da sau 2π radius. Saboda haka, diamita shine rabin zagaye.
Tambaya 4: Teburin da za mu zauna a kai yana da kewayen yadi 6.28. Muna buƙatar nemo diamita na tebur.
A. 1 yadi
B. 2 yarda
C. 3 yadi
D. 4 yarda
✅ Amsa Daidai:
B. 2 yarda
Ƙarin bayani:
Ana ƙididdige zagayen da'irar ta hanyar ninka diamita ta pi (π). A wannan yanayin, an ba da kewaye kamar yadi 6.28. Don nemo diamita, muna buƙatar raba kewaye ta pi. Rarraba yadi 6.28 da pi yana ba mu kusan yadi 2. Saboda haka, diamita na tebur shine yadi 2.
Tambaya ta biyar: Lambun da'ira tana da kewayen mita 5. Menene madaidaicin radius na lambun?
A. 3.14 mita
B. 6 mita
C. 9 mita
D. 18m
✅ Amsa Daidai:
C. 9 mita
Ƙarin bayani:
Don nemo radius, yi amfani da dabara don kewaye: C = 2πr. Sake tsara dabara don warware radius: r = C / (2π). Toshe cikin da'irar da aka bayar na mita 36 da amfani da kimar kimar π kamar 3.14, kuna samun r = 36 / (2 * 3.14) ≈ 9 mita.
Tambaya ta shida: Wurin ninkaya madauwari yana da radius na mita 6. Menene kusan tazarar da mai iyo ke tafiya a kusa da tafkin yayin da yake kammala ƙafa ɗaya?
A. 16 mita
B. 25 mita
C. 50 mita
D. 100m
✅ Amsa Daidai:
C. 50 mita
Ƙarin bayani:
Don nemo tazarar da mai iyo ke tafiya a kusa da tafkin don cinya ɗaya, kuna amfani da tsarin kewaya (C = 2πr). A wannan yanayin, yana da 2 * 3.14 * 8 mita ≈ 50.24 mita, wanda ya kai kimanin mita 50.
Tambaya Ta bakwai Lokacin da ake auna hula hoop a aji, rukunin C ya gano cewa tana da radius inci 7. Menene kewayen hula hoop?
A. 39.6 inci
B. 37.6 inci
C. 47.6 inci
D.49.6 inci
✅ Amsa Daidai:
C. 47.6 inci
Ƙarin bayani:
Ana iya samun kewayen da'irar ta amfani da dabara C = 2πr, inda r shine radius na da'irar. A wannan yanayin, ana ba da radius na hula hoop kamar inci 7. Haɗa wannan ƙimar cikin dabara, muna samun C = 2π(7) = 14π inci. Kimanin π zuwa 3.14, za mu iya lissafin kewaye kamar 14(3.14) = 43.96 inci. Idan aka zagaya zuwa kashi na goma mafi kusa, kewayen shine inci 47.6, wanda yayi daidai da amsar da aka bayar.
Tambaya Ta Takwas: Semi da'ira tana da radius na mita 8. Menene kewayenta?
A. 20 mita
B. 15 mita
C. 31.42 mita
D. 62.84m
✅ Amsa Daidai:
C. 31.42 mita
Ƙarin bayani: Don nemo kewayen da'irar, lissafta rabin da'irar cikakken da'irar tare da radius na mita 10.
Tambaya ta 9: Ƙwallon kwando suna wasa da ball mai radius 5.6 inci. Menene kewayen kowace kwando?
A. 11.2 inci
B. 17.6 inci
C. 22.4 inci
D.35.2 inci
✅ Amsa Daidai:
C. 22.4 inci
Bayani:
Kuna iya amfani da dabara don kewaya da'irar, wanda shine C = 2πr. Radius da aka bayar shine inci 5.6. Toshe wannan darajar cikin dabara, muna da C = 2π * 5.6 inci. C ≈ 2 * 3.14 * 5.6 inci. C ≈ 11.2 * 5.6 inci. C ≈ 22.4 inci. Don haka, kewayen kowane kwando yana da kusan inci 22.4. Wannan yana wakiltar nisa a kusa da kwando.
Tambaya ta 10: Saratu da ƙawayenta guda biyu suna gina tebur na fiffike da'ira don taronsu. Sun san cewa domin dukansu su zauna cikin kwanciyar hankali a kusa da teburin, suna buƙatar kewayen ƙafa 18. Wane diamita dole ne tebur ɗin wasan ya kasance yana da shi don cimma daidaitaccen kewaye?
A. 3 ƙafa
B. 6 ƙafa
C. 9 kafa
D. 12 kafa
✅ Amsa Daidai:
B. 6 ƙafa
Ƙarin bayani:
Don nemo radius, raba kewaye da 2π, muna da r = C / (2π) r = 18 ƙafa / (2 * 3.14) r ≈ 18 ƙafa / 6.28 r ≈ 2.87 ƙafa (an zagaye zuwa kashi dari mafi kusa).
Yanzu, don nemo diamita, kawai ninka radius: Diamita = 2 * Diamita Radius ≈ 2 * 2.87 ƙafa Diamita ≈ 5.74 ƙafa. Don haka, teburin fikin dole ne ya sami diamita na kusan ƙafa 5.74
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Tambayoyin da
Menene 2πr na da'ira?
2πr shine ma'anar kewayawar da'irar. A cikin wannan tsari:
- "2" yana wakiltar cewa kana ɗaukar tsawon radius sau biyu. Da'irar ita ce tazarar da'irar, don haka kuna buƙatar zagaya da'irar sau ɗaya kuma sau ɗaya, wanda shine dalilin da ya sa muke ninka da 2.
- "π" (pi) mathematics akai akai kusan 3.14159. Ana amfani da shi saboda yana wakiltar alakar da'irar da diamita na da'irar.
- "r" yana wakiltar radius na da'irar, wanda shine nisa daga tsakiyar da'irar zuwa kowane wuri akan kewayensa.
Me yasa kewaye yake 2πr?
Dabarar kewayawar da'irar, C = 2πr, ta fito ne daga ma'anar pi (π) da kaddarorin lissafi na da'ira. Pi (π) yana wakiltar rabon kewayen da'irar zuwa diamita. Lokacin da kuka ninka radius (r) da 2π, da gaske kuna ƙididdige nisan da'irar, wanda shine ma'anar kewaye.
Shin kewayawa sau 3.14 shine radius?
A'a, kewayen ba daidai ba ne sau 3.14 na radius. Dangantakar da ke tsakanin kewayawa da radius na da'irar ana bayar da ita ta hanyar dabara C = 2πr. Yayin da π (pi) ya kai kusan 3.14159, kewayen shine sau 2 π sau radius. Don haka, kewaye ya fi sau 3.14 kawai radius; sau 2 ne π sau radius.
Ref: Omni Caculator | Prof
