Kamano pakeng tsa Bolelele ba Arc le Sebaka sa Sector
Lipalong, haholo-holo jeometring ea sefofane, ho na le likhopolo tsa bohlokoa tse amanang le li-circle. Likhopolo tse peli tsa bohlokoa tse tšohloang khafetsa ke bolelele ba arc le sebaka sa sector. Kutloisiso e ntle ea likhopolo tsena tse peli e re lumella ho bala likarolo tse fapaneng tsa li-circle, ebang ke lithutong tse akaretsang tsa lipalo, lits'ebetsong tsa tekheniki, kapa bophelong ba letsatsi le letsatsi.
Tlhaloso ea Selikalikoe
Pele re tsoela pele, ho molemo ho utloisisa hore na selikalikoe ke eng. Selikalikoe ke sete sa lintlha tsohle tse sefofaneng tse leng sebaka se tsitsitseng ho tloha ntlheng e itseng e bitsoang setsi. Sebaka sena se tsitsitseng se tsejoa e le radius ea selikalikoe. Selikalikoe se na le likarolo tse 'maloa tsa bohlokoa, ho kenyeletsoa:
1. Ntlha e Bohareng (O): Ntlha e tsitsitseng eo ho yona ho lekanngwang bolelele ba dintlha tse ding tsohle tse ka hara selikalikoe.
2. Radius (r): Sebaka ho tloha ntlheng e bohareng ho ea ntlheng efe kapa efe selikalikoeng.
3. Bophara (d): Sebaka se selelele ka ho fetisisa ho tloha ntlheng e 'ngoe ho ea ho e 'ngoe holim'a selikalikoe se fetang ntlheng e bohareng. Bophara bo habeli ba bolelele ba radius.
4. Selika-likoe (C): Bolelele ba mola o potileng selikalikoe, bo baloang ho sebelisoa foromo \( C = 2 \pi r \).
Ho Utloisisa Bolelele ba Arc
Bolelele ba arc ke bolelele ba karolo e itseng ea selikalikoe sa selikalikoe. A re nahaneng ka selikalikoe se seholo se khaotsoeng ka mela e 'meli ea radial. Mela ena ea radial e arola selikalikoe ka li-arcs tse peli, tseo re li bitsang li-arcs tse kholo le tse nyane, ho latela bolelele ba tsona.
Ho bala bolelele ba arc, re hloka ho tseba radius ea selikalikoe le boholo ba sekhutlo se bohareng se entsoeng ke mela e 'meli ea radial. Bolelele ba arc bo ka baloa ho sebelisoa foromo:
\[ L = \theta \times r \]
Moo:
– \( L \) ke bolelele ba arc,
– \( \theta \) ke sekhutlo se bohareng ka har'a li-radian,
– \( r \) ke radius ya sedikadikwe.
Haeba sekhutlo se bohareng se le ka di-degree, foromo e fetoha ho:
\[ L = \left( \frac{\theta}{360} \right) \times 2 \pir \]
Mohlala, haeba o na le selikalikoe se nang le radius ea liyuniti tse 10 le sekhutlo se bohareng sa likhato tse 60, bolelele ba arc bo ka baloa ka tsela ena:
\[ L = \left( \frac{60}{360} \right) \times 2 \pi \times 10 = \left( \frac{1}{6} \right) \times 20 \pi = \frac{20 \pi}{6} \hoo e ka bang 10.47 \, \text{unit} \]
Tlhaloso ea Sebaka sa Lekala
Sebaka sa lekala ke sebaka sa karolo e itseng ea selikalikoe se entsoeng ka mela e 'meli ea radial le arc e li hokahanyang. Makala hangata a bapisoa le likarolo tsa phae kapa pizza. Ho bala sebaka sa lekala, re hloka radius ea selikalikoe le sekhutlo se bohareng se entsoeng ke mela e 'meli ea radial.
Foromo ea ho bala sebaka sa lekala ke:
\[ A = \frac{1}{2} r^2 \theta \]
Moo:
– \( A \) ke sebaka sa lekala,
– \( \theta \) ke sekhutlo se bohareng ka har'a li-radian,
– \( r \) ke radius ya sedikadikwe.
Haeba sekhutlo se bohareng se le ka di-degree, foromo e fetoloa ho:
\[ A = \left( \frac{\theta}{360} \right) \times \pi r^2 \]
Mohlala, ha re re re na le selikalikoe se nang le radius ea li-unit tse 10 le sekhutlo se bohareng sa likhato tse 60. Ebe sebaka sa lekala se ka baloa ka tsela ena:
\[ A = \left( \frac{60}{360} \right) \times \pi \times 10^2 = \left( \frac{1}{6} \right) \times 100 \pi = \frac{100 \pi}{6} \hoo e ka bang 52.36 \, \text{unit}^2 \]
Kamano Pakeng tsa Bolelele ba Arc le Sebaka sa Lekala
Mehopolo ea bolelele ba arc le sebaka sa sector li amana haufi-ufi hobane ka bobeli li itšetlehile ka radius ea selikalikoe le sekhutlo se bohareng. Ka ho tseba e 'ngoe ea tsena tse peli le tlhahisoleseling e eketsehileng joalo ka radius kapa sekhutlo se bohareng, re ka bala e 'ngoe.
Kamano ea lipalo pakeng tsa bolelele ba arc le sebaka sa lekala e ka etsoa ka tsela e latelang. Ho tsoa foromong eo re seng re ntse re e tseba:
1. Bolelele ba Arc: \[ L = \left( \frac{\theta}{360} \right) \times 2 \pir \]
2. Sebaka sa letlooa: \[ A = \left( \frac{\theta}{360} \right) \times \pi r^2 \]
Re ka bona ho tsoa liforomong tse peli tse kaholimo hore ho na le ho tšoana karolong ea angular \(\left( \frac{\theta}{360} \right)\) e bontšang karolo ea selikalikoe sohle se entsoeng.
Haeba re batla ho hokahanya tse peli ho ea pele, hlokomela hore bolelele ba arc \( L \) ke peresente ea selikalikoe sa selikalikoe 'me sebaka sa sector \( A \) ke peresente ea sebaka sa selikalikoe. Ka mantsoe a mang,
\[ L = \left( \frac{\theta}{360} \right) \times 2 \pir \]
\[ A = \left( \frac{L}{2 \pi r} \right) \times \pi r^2 \]
Nolofatsa likaroloana,
\[ A = \left( \frac{L}{2} \right) \times r \]
Kahoo re ka bolela ka ho toba hore, sebaka sa lekala se ka amana le bolelele ba arc ho pholletsa le bolelele ba arc le radius:
\[ A = \frac{1}{2} L r \]
Litšebeliso Bophelong ba Letsatsi le Letsatsi
Ho utloisisa kamano pakeng tsa bolelele ba arc le sebaka sa lekala ha se thuto feela, empa hape ho na le lits'ebetso tse sebetsang likarolong tse fapaneng tsa bophelo ba letsatsi le letsatsi. Tse ling tsa lits'ebetso tsena li kenyelletsa:
1. Moralo oa Meaho: Ha ho raloa mehaho kapa meaho e chitja, joalo ka mathule, lirapa, kapa meaho e chitja, ho bala bolelele ba arc le sebaka sa lekala ho bohlokoa haholo.
2. Boenjiniere ba Mekaniki: Ha ho raloa likarolo tsa mochini tse kenyeletsang motsamao o chitja kapa o moqotetsane, tsebo ena e thusa ho bala litsela le libaka tse hlokahalang.
3. Bolepi ba linaleli: Ha ho etsoa mohlala oa litsela tsa lipolanete kapa li-satellite tsa tlhaho tse chitja kapa tse potoaneng.
4. Temo: E thusa ho rala nosetso ea setsi ho netefatsa hore metsi a ajoa ka ho lekana.
Qetello
Ho utloisisa kamano pakeng tsa bolelele ba arc le sebaka sa lekala ho re thusa ho utloisisa hamolemo kamoo likhutlo, radii, le likarolo tse ling tsa selikalikoe li sebelisanang kateng. Ka ho sebelisa mekhoa ena ea motheo, re ka sebetsana le liphephetso tse fapaneng lipalo tsa jeometri hammoho le lits'ebetso tse sebetsang masimong a fapaneng, ho kenyeletsoa meralo ea meaho, boenjiniere, temo le bolepi ba linaleli. Mehopolo ena e 'meli, leha e bonahala e le bonolo, e na le lits'ebetso tse pharaletseng bophelong bohle ba letsatsi le letsatsi, e leng se etsang hore e be ea bohlokoa ho ithuta le ho tseba.
