Muenzaniso weMubvunzo weKukurukurirana paCircular Arcs
Mukuongorora geometry, denderedzwa imufananidzo wakaita sedenderedzwa une pfungwa dzakawanda dzinonakidza dzekudzidza, imwe yacho idenderedzwa. Arc chikamu chemucheto wedenderedzwa chiri pakati pemapoinzi maviri padenderedzwa. Muchinyorwa chino, tichaongorora matambudziko akasiyana-siyana ane chekuita nedenderedzwa.
Kunzwisisa Kwekutanga kweCircular Arcs
Usati waenderera mberi nemibvunzo yemuenzaniso, zvakakosha kutanga wanzwisisa pfungwa dzinokosha:
1. Denderedzwa:
Denderedzwa muunganidzwa wemapoinzi ese ari mudenderedzwa ari kure zvakaenzana kubva panzvimbo yepakati.
2. Nharaunda (Minwe):
Radiyo (radius) zvinoreva daro kubva pakati pedenderedzwa kusvika chero panzvimbo iri kumucheto kwedenderedzwa.
3. Dhayamita:
Dhayamita ndiyo daro refu kubva pane imwe nzvimbo iri kumucheto kwedenderedzwa kuenda kune imwe nzvimbo iri kudivi rakapesana nepakati. Dhayamita yacho yakapetwa kaviri radius.
4. Kukotama:
Arc chikamu chemucheto wedenderedzwa. Kana mapoinzi A naB ari pamucheto wedenderedzwa, saka arc AB chikamu chedenderedzwa riri pakati paA naB.
Mafomura Akabatana neArcs of Circles
Kuti tinzwisise urefu hwe arc, tinofanira kunzwisisa mafomura akati wandei:
1. Kureba kweArc (L):
Kureba kwedenderedzwa remupendero ndiko kureba kwemupendero wedenderedzwa rine mupendero wedenderedzwa. Fomura yacho ndeiyi:
\[
L = r \nguva \theta
\]
apo \( r \) iri radius yedenderedzwa uye \( \theta \) iri kona yepakati muma radians inopindirana ne arc.
2. Kureba kweArc muDhigirii:
Kana kona yepakati iri mumadhigirii, tinoshandisa fomura iyi:
\[
L = \frac{\theta}{360^\circ} \times 2\pir r
\]
apo \( \theta \) iri kona yepakati mumadhigirii.
Mibvunzo yemuenzaniso nekukurukurirana
Mubvunzo 1: Kuverenga Hurefu hweArc
Mubvunzo:
Denderedzwa rine dhayamita ye10 cm. Verengai kureba kwearc iri pasi pekona yepakati ye60 degrees.
Kukurukurirana:
– Nharaunda yedenderedzwa (\( r \)) = 10 cm
– Kona yepakati (\( \theta \)) = 60°
Kushandisa fomura yekureba kwearc mumadhigirii:
\[
L = \frac{\theta}{360^\circ} \nguva 2 \pi r
\]
\[
L = \frac{60^\circ}{360^\circ} \times 2 \pi \times 10 \text{ cm}
\]
\[
L = \frac{1}{6} \times 2 \pi \times 10 \text{cm}
\]
\[
L = \frac{20\pi}{6} \text{ cm}
\]
\[
L \inenge 10.47 \text{cm}
\]
Saka, kureba kwe arc kunenge 10.47 cm.
Mubvunzo 2: Kuziva Angle Yepakati Kubva Paurefu hweArc
Mubvunzo:
Kana zvataurwa, denderedzwa rine radius ye 14 cm rine arc kureba kwe 22 cm. Sarudza kona yepakati inopindirana arc nemadhigirii.
Kukurukurirana:
– Nharaunda yedenderedzwa (\( r \)) = 14 cm
– Kureba kwe arc (\( L \)) = 22 cm
Shandisa fomura ye arc length kuti uwane \( \theta \):
\[
L = \frac{\theta}{360^\circ} \nguva 2 \pi r
\]
Tsiva tsika dzinozivikanwa:
\[
22 = \frac{\theta}{360^\circ} \nguva 2 \pi \nguva 14
\]
Kuzviparadzanisa \( \theta \):
\[
22 = \frac{\theta}{360^\circ} \nguva 28 \pi
\]
\[
22 \nguva 360^\circ = \theta \nguva 28 \pi
\]
\[
7920 = \theta \nguva 28 \pi
\]
\[
\theta = \frac{7920}{28 \pi}
\]
\[
\theta \inenge 90.72^\circ
\]
Saka, saizi yekona yepakati inenge madhigirii 90.72.
Mubvunzo 3: Kuverenga Nzvimbo yeSector
Mubvunzo:
Chikamu chedenderedzwa chinoumbwa nekona yepakati yemadhigirii 120 neredhiyo ye7 cm. Sarudza nzvimbo yechikamu chacho.
Kukurukurirana:
– Nharaunda yedenderedzwa (\( r \)) = 7 cm
– Kona yepakati (\( \theta \)) = 120°
Shandisa fomura yenzvimbo yechikamu:
\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]
Tsiva tsika dzinozivikanwa:
\[
A = \frac{120^\circ}{360^\circ} \times \pi \times 7^2
\]
\[
A = \frac{1}{3} \nguva \pi \nguva 49
\]
\[
A = \frac{49\pi}{3}
\]
\[
A \approx 51.43 \text{ cm}^2
\]
Saka, nzvimbo yechikamu ichi inenge 51.43 cm².
Mubvunzo 4: Kuona Arc kubva kuNzvimbo yeSector
Mubvunzo:
Nzvimbo yechikamu chedenderedzwa chine radius ye6 cm i18π cm². Hurefu hwe arc yechikamu ndehupi?
Kukurukurirana:
– Nharaunda yedenderedzwa (\( r \)) = 6 cm
– Nzvimbo yechikamu (\( A \)) = 18π cm²
Shandisa fomura yenzvimbo yechikamu kuti uwane kona yepakati \( \theta \):
\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]
Tsiva tsika dzinozivikanwa:
\[
18\pi = \frac{\theta}{360^\circ} \nguva \pi \nguva 6^2
\]
\[
18\pi = \frac{\theta}{360^\circ} \nguva 36\pi
\]
\[
18 = \frac{\theta}{360^\circ} \nguva 36
\]
\[
18 \nguva 360^\circ = \theta \nguva 36
\]
\[
6480 = \theta \nguva 36
\]
\[
\theta = \frac{6480}{36}
\]
\[
\theta = 180^\denderedzwa
\]
Zvino, nekona yepakati yemadhigirii 180, tinosarudza kureba kwearc:
\[
L = \frac{\theta}{360^\circ} \nguva 2 \pi r
\]
\[
L = \frac{180^\circ}{360^\circ} \nguva 2 \pi \nguva 6
\]
\[
L = \frac{1}{2} \kawa 2 \pi \kawa 6
\]
\[
L = \pi \kawa 6
\]
\[
L \inenge 18.85 \text{cm}
\]
Saka, kureba kweuta kunenge 18.85 cm.
Mhedziso
Kunzwisisa ma arc akatenderera uye maverengerwo awo ihwaro hwakakosha mu geometry nemasvomhu zvakazara. Kuburikidza nemienzaniso yakakurukurwa munyaya ino, vaverengi vanotarisirwa kuwana kunzwisisa kuri nani kwekuverenga kureba kwe arc, nzvimbo yechikamu, uye kuona kona yepakati inopindirana ne arc. Kunzwisisa kwakanaka kwepfungwa idzi dzekutanga kuchabatsira zvikuru mukugadzirisa matambudziko akasiyana-siyana ane chekuita nema denderedzwa.
