Mohlala oa Potso ea Puisano mabapi le Li-Circular Arcs
Ho jiometri, selikalikoe ke setšoantšo se bataletseng se nang le mehopolo e mengata e khahlisang eo ho ka ithutoang eona, e 'ngoe ea eona ke selikalikoe. Selikalikoe ke karolo ea moeli oa selikalikoe e pakeng tsa lintlha tse peli selikalikoeng. Sehloohong sena, re tla hlahloba mathata a fapaneng a mehlala le litharollo tsa 'ona tse amanang le li-arcs.
Kutloisiso ea Motheo ea Li-Arc tse Selikalikoe
Pele o fetela lipotsong tsa mohlala, ho bohlokoa ho utloisisa likhopolo tse ling tsa motheo pele:
1. Selikalikoe:
Selikalikoe ke pokello ea lintlha tsohle tse ka har'a sefofane tse hole ka ho lekana le ntlha e bohareng e fanoeng.
2. Radius (Menoana):
Radius ke sebaka se tlohang bohareng ba selikalikoe ho ea ntlheng efe kapa efe e moeling oa selikalikoe.
3. Bophara:
Bophara ke sebaka se selelele ka ho fetisisa ho tloha ntlheng e 'ngoe e ka lehlakoreng la selikalikoe ho ea ntlheng e 'ngoe ka lehlakoreng le leng ho pholletsa le bohareng. Bophara bo habeli ba radius.
4. Seqha:
Arc ke karolo ea moeli oa selikalikoe. Haeba lintlha A le B li le moeling oa selikalikoe, joale arc AB ke karolo ea selikalikoe pakeng tsa A le B.
Liforomo tse Amanang le Li-Arcs tsa Li-Circles
Ho lekanya bolelele ba arc, re hloka ho utloisisa mekhoa e 'maloa:
1. Bolelele ba Arc (L):
Bolelele ba arc e chitja ke bolelele ba moedi wa sedikadikwe o kenyeletsang arc. Foromo ke:
\[
L = r \times \theta
\]
moo \( r \) e leng radius ea selikalikoe le \( \theta \) e leng sekhutlo se bohareng sa radians se kopanang le arc.
2. Bolelele ba Arc ka Dikereiti:
Haeba sekhutlo se bohareng se le ka di-degree, re sebedisa foromo:
\[
L = \frac{\theta}{360^\circ} \times 2\pir r
\]
moo \( \theta \) e leng sekhutlo se bohareng ka di-degree.
Lipotso tsa Mehlala le Puisano
Potso ea 1: Ho Bala Bolelele ba Arc
Potso:
Selikalikoe se na le radius ea 10 cm. Bala bolelele ba arc e ka tlas'a sekhutlo se bohareng sa likhato tse 60.
Puisano:
– Radius ea selikalikoe (\( r \)) = 10 cm
– Sekhutlo se bohareng (\( \theta \)) = 60°
Ho sebelisa foromo ea bolelele ba arc ka li-degrees:
\[
L = \frac{\theta}{360^\circ} \times 2 \pi r
\]
\[
L = \frac{60^\circ}{360^\circ} \times 2 \pi \times 10 \text{ cm}
\]
\[
L = \frac{1}{6} \times 2 \pi \times 10 \text{cm}
\]
\[
L = \frac{20\pi}{6} \text{ cm}
\]
\[
L \hoo e ka bang 10.47 \mongolo{cm}
\]
Kahoo, bolelele ba arc ke hoo e ka bang 10.47 cm.
Potso ea 2: Ho Fumana Sekhutlo se Bohareng ho tloha Bolelele ba Arc
Potso:
Ha ho fanoe ka selikalikoe se nang le radius ea 14 cm, bolelele ba arc ke 22 cm. Fumana sekhutlo se bohareng se kopanang le arc ka likhato.
Puisano:
– Radius ea selikalikoe (\( r \)) = 14 cm
– Bolelele ba arc (\( L \)) = 22 cm
Sebelisa foromo ea bolelele ba arc ho fumana \( \theta \):
\[
L = \frac{\theta}{360^\circ} \times 2 \pi r
\]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[
22 = \frac{\theta}{360^\circ} \times 2 \pi \times 14
\]
Ho itšehla thajana \( \theta \):
\[
22 = \frac{\theta}{360^\circ} \times 28 \pi
\]
\[
22 \ka makhetlo a 360^\circ = \theta \ka makhetlo a 28 \pi
\]
\[
7920 = \theta \makgetlo a 28 \pi
\]
\[
\theta = \frac{7920}{28 \pi}
\]
\[
\theta \hoo e ka bang 90.72^\circ
\]
Kahoo, boholo ba sekhutlo se bohareng ke hoo e ka bang likhato tse 90.72.
Potso ea 3: Ho Bala Sebaka sa Lekala
Potso:
Karolo ea selikalikoe e thehoa ka sekhutlo se bohareng sa likhato tse 120 ka radius ea 7 cm. Fumana sebaka sa karolo eo.
Puisano:
– Radius ea selikalikoe (\( r \)) = 7 cm
– Sekhutlo se bohareng (\( \theta \)) = 120°
Sebelisa foromo bakeng sa sebaka sa lekala:
\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[
A = \frac{120^\circ}{360^\circ} \times \pi \times 7^2
\]
\[
A = \frac{1}{3} \times \pi \times 49
\]
\[
A = \frac{49\pi}{3}
\]
\[
A \hoo e ka bang 51.43 \mongolo{cm}^2
\]
Kahoo, sebaka sa lekala lena ke hoo e ka bang 51.43 cm².
Potso ea 4: Ho Fumana Arc ho tloha Sebakeng sa Lekala
Potso:
Sebaka sa karolo e chitja e nang le radius ea 6 cm ke 18π cm². Bolelele ba arc ea karolo ke bofe?
Puisano:
– Radius ea selikalikoe (\( r \)) = 6 cm
– Sebaka sa lekala (\( A \)) = 18π cm²
Sebelisa foromo ea sebaka bakeng sa lekala ho fumana sekhutlo se bohareng \( \theta \):
\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[
18\pi = \frac{\theta}{360^\circ} \times \pi \times 6^2
\]
\[
18\pi = \frac{\theta}{360^\circ} \times 36\pi
\]
\[
18 = \frac{\theta}{360^\circ} \times 36
\]
\[
18 \ka makhetlo a 360^\circ = \theta \ka makhetlo a 36
\]
\[
6480 = \theta \makhetlo a 36
\]
\[
\theta = \frac{6480}{36}
\]
\[
\theta = 180^\circle
\]
Jwale, ka sekhutlo se bohareng sa di-degree tse 180, re fumana bolelele ba arc:
\[
L = \frac{\theta}{360^\circ} \times 2 \pi r
\]
\[
L = \frac{180^\circ}{360^\circ} \times 2 \pi \times 6
\]
\[
L = \frac{1}{2} \makgetlo a 2 \pi \makgetlo a 6
\]
\[
L = \pi \ makhetlo a 6
\]
\[
L \hoo e ka bang 18.85 \mongolo{cm}
\]
Kahoo, bolelele ba seqha bo ka ba 18.85 cm.
Qetello
Ho utloisisa li-arc tse chitja le mokhoa oa ho li bala ke motheo oa bohlokoa oa jeometri le lipalo ka kakaretso. Ka mehlala e tšohliloeng sehloohong sena, babali ba lebelletsoe ho utloisisa hamolemo mokhoa oa ho bala bolelele ba arc, sebaka sa karolo, le ho fumana sekhutlo se bohareng se kopanang le arc. Kutloisiso e ntle ea likhopolo tsena tsa motheo e tla ba thuso haholo ho rarolleng mathata a fapaneng a amanang le li-circles.
