Nzira yekuverenga sei Circumference yedenderedzwa chaizvo?
Denderedzwa yedenderedzwa ruzivo rwekutanga uye rwunodiwa rwemasvomhu rwakaunzwa muchikoro chepuraimari kana chepakati. Kuziva denderedzwa redenderedzwa kwakakosha kuvadzidzi vanoronga kuita mamwe makosi epamusoro masvomhu muchikoro chesekondari uye kukoreji uye kugadzirira bvunzo dzakamira seSAT uye ACT.
Denderedzwa gumi reMibvunzo yeDenderedzwa muchinyorwa chino rakagadzirirwa kuyedza kunzwisisa kwako kwekutsvaga radius, dhayamita, uye denderedzwa redenderedzwa.
Zviri Mukati:
Circumfence yedenderedzwa fomula
Tisati tatora bvunzo, ngatidzokororei rumwe ruzivo rwakakosha!
Chii chinonzi denderedzwa?
Denderedzwa redenderedzwa ndiro nhambwe yemutsara yemucheto wedenderedzwa. Iyo yakaenzana neperimeter ye geometric shape, kunyange zvazvo izwi rekuti perimeter rinongoshandiswa kumapolygoni.
Nzira yekuwana sei denderedzwa redenderedzwa?
The denderedzwa redenderedzwa formula ndeiyi:
C = 2πr
kupi:
- C ndiyo denderedzwa
- π (pi) inhambo yemasvomhu inongogara yakaenzana ne3.14159
- r ndiyo radius yedenderedzwa
Nharaunda (radius) inhambwe kubva pakati pedenderedzwa kusvika kune chero nzvimbo iri kumucheto.
Iyo dhayamita yakapetwa kaviri radius, saka iyo denderedzwa inogona zvakare kuratidzwa se:
C = πd
kupi:
- d ndiyo dhayamita
Semuenzaniso, kana radius yedenderedzwa iri 5 cm, ipapo denderedzwa ndeiyi:
C = 2πr = 2π * 5 cm = 10π cm
≈ 31.4 cm (yakatenderedzwa kusvika 2 decimal nzvimbo)
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Denderedzwa remibvunzo yedenderedzwa
Mubvunzo wekutanga: Kana denderedzwa redziva rekutuhwina riri 1 metres, radius yaro ndeipi?
A. 7.95 mamita
B. 8.00 mamita
C. 15.91 mamita
D. 25 mamita
✅ Mhinduro Yechokwadi:
A. 7.95 mamita
Tsanangudzo:
Iyo radius inogona kuwanikwa nekugadzirisa zvakare fomula C = 2πr uye kugadzirisa r: r = C / (2π). Kurovera mudenderedzwa rakapihwa remamita makumi mashanu uye kupotsa π kusvika 50, tinowana radius ingangoita 3.14 metres.
Mubvunzo 2: Kureba kwedenderedzwa inches gumi nemana. Chii chinonzi radius yayo?
A. 28 inches
B.14 inches
C. 21 inches
D. masendimita manomwe
✅ Mhinduro Yechokwadi:
D. masendimita manomwe
Tsanangudzo:
Sezvo dhayamita yakapetwa kaviri kureba kweradius (d = 2r), unogona kuwana radius nekukamura dhayamita ne2 (r = d / 2) kureba kwe14 inches.
Mubvunzo 3: Ndechipi chezvirevo zvinotevera chechokwadi pamusoro pehukama pakati pedhayamita nedenderedzwa redenderedzwa?
A. The dhayamita ihafu yedenderedzwa.
B. Dzungu rakafanana nedenderedzwa.
C. Dzungu rakapetwa kaviri denderedzwa.
D. Dzungu ndiro π nguva yedenderedzwa.
✅ Mhinduro Yechokwadi:
A. The dhayamita ihafu yedenderedzwa.
Tsanangudzo:
Dzungu rakaenzana ne 2 times the radius, ukuwo denderedzwa rakaenzana ne 2π times the radius. Naizvozvo, dhayamita ihafu yedenderedzwa.
Mubvunzo wechina: Tafura yatinofanira kugara ine denderedzwa remayadhi 4. Tinofanira kuwana dhayamita yetafura.
A. 1 yadhi
B. 2 mayadhi
C. mamita matatu
D. mayadhi mana
✅ Mhinduro Yechokwadi:
B. 2 mayadhi
Tsanangudzo:
Denderedzwa redenderedzwa rinoverengwa nekuwanza dhayamita nepi (π). Muchiitiko ichi, denderedzwa inopiwa semayadhi 6.28. Kuti tiwane dhayamita, tinofanira kupatsanura denderedzwa ne pi. Kupatsanura 6.28 mayadhi nepi kunotipa angangoita mayadhi maviri. Naizvozvo, dhayamita yetafura ndeye 2 mayadhi.
Mubvunzo wechishanu: Gadheni rine denderedzwa rine denderedzwa remamita makumi matatu nematanhatu. Ndeipi inenge radius yebindu?
A. 3.14 mamita
B. 6 mamita
C. 9 mamita
D. 18 mamita
✅ Mhinduro Yechokwadi:
C. 9 mamita
Tsanangudzo:
Kuti uwane radius, shandisa fomula yekutenderera: C = 2πr. Rongedza zvakare fomula yekugadzirisa yeradius: r = C / (2π). Kupinza denderedzwa rakapihwa remamita makumi matatu nematanhatu uye uchishandisa kukosha kwe π se 36, unowana r = 3.14 / (36 * 2) ≈ 3.14 metres.
Mubvunzo wechitanhatu: Dziva rekutuhwina rine denderedzwa rine radius yemamita masere. Ndeipi nhanho inosvika nhambwe inofambwa nemutuhwi achipoterera dziva kana achinge apedza chikamu chimwe chete?
A. 16 mamita
B. 25 mamita
C. 50 mamita
D. 100 mamita
✅ Mhinduro Yechokwadi:
C. 50 mamita
Tsanangudzo:
Kuti uwane chinhambwe chinofambwa nemutuhwi achitenderedza dziva pamakumbo mamwe chete, unoshandisa fomula yedenderedzwa (C = 2πr). Muchiitiko ichi, 2 * 3.14 * 8 mamita ≈ 50.24 mamita, iyo inenge 50 mamita.
Mubvunzo wechinomwe: Pakuyera hula hoop mukirasi, boka C rakaona kuti rakanga riine radius yemainji manomwe. Ndeipi denderedzwa yehula hoop?
A. 39.6 inches
B. 37.6 inches
C. 47.6 inches
D. masendimita manomwe
✅ Mhinduro Yechokwadi:
C. 47.6 inches
Tsanangudzo:
Denderedzwa redenderedzwa rinogona kuwanikwa uchishandisa formula C = 2πr, apo r ndiyo radius yedenderedzwa. Muchiitiko ichi, radius ye hula hoop inopiwa se 7 inches. Kubatanidza kukosha uku mufomula, tinowana C = 2π(7) = 14π inches. Kusvika π kusvika 3.14, tinogona kuverenga denderedzwa se 14(3.14) = 43.96 inches. Yakatenderedzwa kusvika pachikamu chegumi chiri pedyo, denderedzwa iri 47.6 inches, inofanana nemhinduro yakapihwa.
Mubvunzo wechisere: Semicircle ine radius yemamita gumi. Chii chinonzi perimeter?
A. 20 mamita
B. 15 mamita
C. 31.42 mamita
D. 62.84 mamita
✅ Mhinduro Yechokwadi:
C. 31.42 mamita
Tsanangudzo: Kuti uwane perimeter ye semicircle, verenga hafu yedenderedzwa redenderedzwa rakazara rine radius yemamita gumi.
Mubvunzo wechipfumbamwe: Chikwata chebasketball chinotamba nebhora rine radius ye9 inches. Ndeipi denderedzwa yebasketball yega yega?
A. 11.2 inches
B. 17.6 inches
C. 22.4 inches
D. masendimita manomwe
✅ Mhinduro Yechokwadi:
C. 22.4 inches
Tsanangudzo:
Unogona kushandisa fomula yedenderedzwa redenderedzwa, rinova C = 2πr. Iyo radius yakapihwa ndeye 5.6 inches. Batanidza kukosha uku mufomula, isu tine C = 2π * 5.6 inches. C ≈ 2 * 3.14 * 5.6 inches. C ≈ 11.2 * 5.6 inches. C ≈ 22.4 inches. Saka, denderedzwa rebhasikiti rega rega rinenge 22.4 inches. Izvi zvinomiririra chinhambwe chakatenderedza basketball.
Mubvunzo wechigumi: Sarah neshamwari dzake mbiri vaigadzira tafura yepikiniki yedenderedzwa yekuungana kwavo. Vaiziva kuti kuti vose vagare zvakanaka vakakomberedza tafura, vaifanira kuita denderedzwa remamita 10. Ndeapi dhayamita rinofanira kuitwa netafura yepikiniki kuti iwane denderedzwa chairo?
A. 3 tsoka
B. 6 tsoka
C. 9 tsoka
D. 12 tsoka
✅ Mhinduro Yechokwadi:
B. 6 tsoka
Tsanangudzo:
Kuti uwane radius, patsanura denderedzwa ne 2π, tine r = C / (2π) r = 18 tsoka / (2 * 3.14) r ≈ 18 tsoka / 6.28 r ≈ 2.87 tsoka (yakatenderedzwa kusvika kuzana repedyo).
Zvino, kuti uwane dhayamita, ingopeta kaviri radius: Diameter = 2 * Radius Diameter ≈ 2 * 2.87 tsoka Diameter ≈ 5.74 tsoka. Saka, tafura yepikiniki inofanira kunge iine dhayamita ingangoita 5.74 tsoka
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Mibvunzo Inonyanya Kubvunzwa
Chii chinonzi 2πr chedenderedzwa?
2πr ndiyo fomula yekutenderera kwedenderedzwa. Mune iyi formula:
- "2" inomiririra kuti uri kutora kaviri kureba kweradius. Denderedzwa ndiro chinhambwe chakatenderedza denderedzwa, saka unofanirwa kutenderera denderedzwa kamwe uyezve, ndosaka tichiwanda ne2.
- “π” (pi) ishoko remasvomhu rinogara richienzana ne3.14159. Inoshandiswa nekuti inomiririra hukama pakati pedenderedzwa uye dhayamita yedenderedzwa.
- “r” inomirira radius yedenderedzwa, inova chinhambwe kubva pakati pedenderedzwa kusvika kune chero nzvimbo iri padenderedzwa.
Sei denderedzwa iri 2πr?
Muteuro wedenderedzwa redenderedzwa, C = 2πr, unobva patsanangudzo yepi (π) uye maitiro ejometri edenderedzwa. Pi (π) inomiririra reshiyo yedenderedzwa kusvika padhayamita rayo. Paunowanza radius (r) na 2π, unotoverenga chinhambwe chakatenderedza denderedzwa, inova tsanangudzo yedenderedzwa.
Ko denderedzwa 3.14 times the radius?
Kwete, denderedzwa haisi chaiyo 3.14 times the radius. Hukama huri pakati pedenderedzwa neradius yedenderedzwa hunopiwa neformula C = 2πr. Nepo π (pi) ichida kuita 3.14159, denderedzwa iri 2 times π times the radius. Saka, denderedzwa rinopfuura 3.14 times the radius; i 2 times π times the radius.
Ref: Omni Caculator | Prof
