Mibvunzo Yemuenzaniso Yekukurukura Madenderedzwa neMakumbo
Denderedzwa chimiro che geometric chinowanzo dzidzwa pamatanho akasiyana edzidzo. Pfungwa iyi haingoshandi chete muzvikoro asiwo inoshandiswa zvakanyanya muhupenyu hwezuva nezuva, senge dhizaini yezvivakwa, mainjiniya emigwagwa, uye kunyangwe hunyanzvi. Chinyorwa chino chichakurukura matambudziko akasiyana-siyana ane chekuita nemadenderedzwa nema arc, pamwe chete nemhinduro dzawo.
Kunzwisisa Madenderedzwa neMadenderedzwa Akatenderera
Denderedzwa muunganidzwa wemapoinzi ese ari mudenderedzwa ari kure zvakaenzana kubva panzvimbo yakatarwa inonzi pakati pedenderedzwa. Daro kubva pakati pedenderedzwa kusvika kune chero nzvimbo iri mudenderedzwa rinonzi radius. Arc yedenderedzwa chikamu chedenderedzwa chakakomberedzwa nemapoinzi maviri padenderedzwa.
Mafomura Ekutanga Aunofanira Kuziva
1. Kutenderera kweDenderedzwa (K):
\[
K = 2 \pi r
\]
apo \( r \) iri nharaunda yedenderedzwa uye \( \pi \approx 3.14 \) kana \( \pi \approx \frac{22}{7} \).
2. Nzvimbo yeDenderedzwa (A):
\[
A = \pi r^2
\]
3. Kureba kweArc:
\[
s = \frac{\theta}{360^\circ} \nguva 2 \pi r
\]
apo \( \theta \) iri kona yepakati mumadhigirii.
4. Nzvimbo yeSector (L):
\[
L = \frac{\theta}{360^\circ} \times \pi r^2
\]
Mibvunzo yemuenzaniso nekukurukurirana
Mubvunzo 1: Kutenderera kweDenderedzwa
Mubvunzo:
Denderedzwa rine dhayamita ye14 cm. Verenga denderedzwa redenderedzwa.
Kukurukurirana:
Kushandisa fomura yekutenderera kwedenderedzwa:
\[
K = 2 \pi r
\]
Kupi \(r = 14 \) cm,
\[
K = 2 \nguva \frac{22}{7} \nguva 14 = 2 \nguva 22 \nguva 2 = 88 \, \text{cm}
\]
Saka, denderedzwa redenderedzwa iri 88 cm.
Mubvunzo 2: Nzvimbo yeDenderedzwa
Mubvunzo:
Kupiwa denderedzwa rine dhayamita ye 10 cm. Verenga nzvimbo yedenderedzwa.
Kukurukurirana:
Kutanga, tinowana nharaunda yedenderedzwa:
\[
r = \frac{d}{2} = \frac{10}{2} = 5 \, \text{cm}
\]
Kushandisa fomura yenzvimbo yedenderedzwa:
\[
A = \pi r^2
\]
\[
A = \pi \nguva 5^2 = \pi \nguva 25 \inenge 3.14 \nguva 25 = 78.5 \, \text{cm}^2
\]
Saka, nzvimbo yedenderedzwa iri 78.5 cm².
Mubvunzo 3: Kureba kweArc Yakatenderera
Mubvunzo:
Denderedzwa rine radius ye 21 cm rine arc inoumba central angle ye 60°. Denderedzwa iri rakareba sei?
Kukurukurirana:
Kushandisa fomura yekureba kwe arc:
\[
s = \frac{\theta}{360^\circ} \nguva 2 \pi r
\]
Kupi \( \theta = 60^\circ \) uye \( r = 21 \, \text{cm} \),
\[
s = \frac{60^\circ}{360^\circ} \nguva 2 \nguva \frac{22}{7} \nguva 21
\]
\[
s = \frac{1}{6} \kawa 2 \kawa \frac{22}{7} \kawa 21
\]
\[
s = \frac{1}{6} \kawa 132 = 22 \, \text{cm}
\]
Saka, kureba kwe arc ndeye 22 cm.
Mubvunzo 4: Nzvimbo yeSector
Mubvunzo:
Verenga nzvimbo yedenderedzwa ine kona yepakati ye90° uye radius ye7 cm.
Kukurukurirana:
Kushandisa fomura yenzvimbo yechikamu:
\[
L = \frac{\theta}{360^\circ} \times \pi r^2
\]
Kupi \( \theta = 90^\circ \) uye \( r = 7 \, \text{cm} \),
\[
L = \frac{90^\circ}{360^\circ} \times \pi \times 7^2
\]
\[
L = \frac{1}{4} \nguva \pi \nguva 49
\]
\[
L = \frac{49 \pi}{4}
\]
\[
L \approx \frac{49 \times 3.14}{4} \approx \frac{153.86}{4} \approx 38.465 \, \text{cm}^2
\]
Saka, nzvimbo yechikamu ichi i38.465 cm².
Mubvunzo 5: Musanganiswa weMibvunzo yeKutenderera neNzvimbo
Mubvunzo:
Denderedzwa rine denderedzwa remasendimita makumi mana nemana. Verenga nzvimbo yedenderedzwa.
Kukurukurirana:
Kutanga, tinowana nharaunda yedenderedzwa tichishandisa fomura yekutenderera:
\[
K = 2 \pi r
\]
Kupi \( K = 44 \, \text{cm} \),
\[
44 = 2 \nguva \frac{22}{7} \nguva r
\]
\[
44 = \frac{44}{7} \times r
\]
\[
r = \frac{44 \kawa 7}{44} = 7 \, \text{cm}
\]
Zvadaro, verenga nzvimbo yedenderedzwa:
\[
A = \pi r^2
\]
\[
A = \pi \nguva 7^2 = \pi \nguva 49 \inenge 3.14 \nguva 49 \inenge 153.86 \, \text{cm}^2
\]
Saka, nzvimbo yedenderedzwa iri 153.86 cm².
Mubvunzo 6: Kuenzanisa Pakati Pemadenderedzwa
Mubvunzo:
Madenderedzwa maviri ane radii ye5 cm uye 10 cm zvakateerana. Sarudza chiyero chedenderedzwa nenzvimbo yemadenderedzwa maviri.
Kukurukurirana:
Kutenderedza:
Kwedenderedzwa rekutanga \( r_1 = 5 \, \text{cm} \):
\[
K_1 = 2 \pi r_1 = 2 \pi \kawa 5 = 10 \pi \, \text{cm}
\]
Kwedenderedzwa rechipiri \( r_2 = 10 \, \text{cm} \):
\[
K_2 = 2 \pi r_2 = 2 \pi \kawa 10 = 20 \pi \, \text{cm}
\]
Kuenzanisa kwemativi:
\[
\frac{K_1}{K_2} = \frac{10 \pi}{20 \pi} = \frac{1}{2}
\]
Yakafara:
Kune denderedzwa rekutanga:
\[
A_1 = \pi r_1^2 = \pi \kawa 5^2 = 25 \pi \, \text{cm}^2
\]
Kwedenderedzwa rechipiri:
\[
A_2 = \pi r_2^2 = \pi \kawa 10^2 = 100 \pi \, \text{cm}^2
\]
Kuenzanisa nzvimbo:
\[
\frac{A_1}{A_2} = \frac{25 \pi}{100 \pi} = \frac{1}{4}
\]
Saka, chiyero chedenderedzwa remadenderedzwa maviri i1:2 uye chiyero chenzvimbo dzawo i1:4.
Mhedziso
Kunzwisisa pfungwa huru nemafomura emadenderedzwa nema arcs kwakakosha pakugadzirisa matambudziko akasiyana-siyana e geometry. Chinyorwa chino chinopa mienzaniso yakawanda yezvinetso nehurukuro kuti usimbise kunzwisisa kwako kwechinyorwa ichi. Matambudziko ekudzidzira uye kunzwisisa kwakadzama zvichakubatsira kushandisa pfungwa idzi munzvimbo dzakasiyana dzekudzidza uye mamiriro chaiwo ehupenyu.
