Lipotso tsa Mehlala le Puisano ea Makala a Selikalikoe
Makala a selikalikoe ke sehlooho sa bohlokoa lipalo tse hlahang khafetsa litlhahlobong le lipotsong tsa boikoetliso. Makala ke karolo ea selikalikoe se moeling oa mahlaseli a mabeli le arc e a hokahanyang. Sehloohong sena, re tla buisana ka mehlala e 'maloa ea mathata makaleng a selikalikoe, hammoho le litlhaloso tse qaqileng, ho tebisa kutloisiso ea rona.
Tlhaloso ea Lekala la Selikalikoe
Lekala la sedikadikwe ke lekala la sedikadikwe le moeditsweng ke di-radii tse pedi le arc e le nngwe. Sebaka sa lekala se balwa ho latela karoloana ya sebaka sohle sa sedikadikwe. Foromo e ka sehloohong e sebediswang ho bala lekala ke ena e latelang:
– Sebaka sa ho Lekola: \[L_juring = \frac{\theta}{360^\circ} \times \pi \times r^2\]
– Bolelele ba Arc: \[P_b = \frac{\theta}{360^\circ} \times 2\pi r\]
Di mana:
– \( \theta \) ke boholo ba sekhutlo sa lekala ka di-degree,
– \( r \) ke radius ea selikalikoe,
– \( \pi \) ke ntho e sa fetoheng (e ka bang 3.14159).
Lipotso tsa Mehlala le Puisano
Potso ea 1:
Fana ka selikalikoe se nang le radius ea 10 cm le lekala le nang le sekhutlo se bohareng sa 90°. Bala sebaka sa lekala.
Puisano:
Hoa tsebahala:
– \(r = 10 \) cm
– \( \theta = 90^\circ \)
Re sebelisa foromo bakeng sa sebaka sa lekala:
\[L_juring = \frac{\theta}{360^\circ} \times \pi \times r^2\]
\[L_juring = \frac{90^\circ}{360^\circ} \times \pi \times (10\text{ cm})^2\]
\[L_juring = \frac{1}{4} \times \pi \times 100\text{ cm}^2\]
\[L_juring = 25\pi\text{ cm}^2\]
Haeba \( \pi \) e nkuwa e le 3.14, joale:
\[L_juring = 25 \makgetlo a 3.14\mongolo{ cm}^2 = 78.5\mongolo{ cm}^2\]
Kahoo, sebaka sa lekala lena ke 78.5 cm².
Potso ea 2:
Karolo ea selikalikoe e na le radius ea 7 cm le bolelele ba arc ea 11 cm. Fumana sekhutlo se bohareng sa karolo ka li-radian.
Puisano:
Hoa tsebahala:
– \(r = 7 \) cm
– Bolelele ba Arc \( P_b = 11 \mongolo{ cm} \)
Re sebelisa foromo ea bolelele ba arc ho fumana angle (theta):
\[P_b = \frac{\theta}{360^\circ} \times 2\pi r\]
Kaha re kopuoa ho fumana sekhutlo ka li-radian, re nkela sebaka sa 360° ka li-radian tsa \(2\pi\):
\[P_b = \theta \times r\]
\[11 = \theta \makgetlo a 7\]
\[\theta = \frac{11}{7}\]
\[\theta \hoo e ka bang 1.57 \text{ rad}\]
Kahoo, sekhutlo se bohareng sa lefapha ke li-radian tse 1.57.
Potso ea 3:
Selikalikoe se nang le radius ea 16 cm se na le lekala le nang le sebaka sa 200 cm². Bala sekhutlo se bohareng sa lekala.
Puisano:
Hoa tsebahala:
– \(r = 16 \) cm
– \( L_juring = 200 \mongolo{cm}^2 \)
Re sebelisa foromo ea sebaka bakeng sa lekala ho fumana \( \theta \):
\[L_juring = \frac{\theta}{360^\circ} \times \pi \times r^2\]
\[200 = \frac{\theta}{360^\circ} \times \pi \times (16)^2\]
\[200 = \frac{\theta}{360^\circ} \times \pi \times 256\]
\[200 = \frac{\theta \times 256 \times \pi}{360^\circ}\]
\[200 \ka makhetlo a 360^\circ = \theta \ka makhetlo a 256 \ka makhetlo a 3.14\]
\[72000 = \theta \makgetlo a 256 \makgetlo a 3.14\]
\[72000 = \theta \makgetlo a 804.64\]
\[\theta = \frac{72000}{804.64}\]
\[\theta \hoo e ka bang 89.45^\circ\]
Kahoo, sekhutlo se bohareng sa lekala ke hoo e ka bang 89.45°.
Potso ea 4:
Bala kakaretso ea selikalikoe sa karolo e nang le radius ea 12 cm le sekhutlo se bohareng sa 120°.
Puisano:
Hoa tsebahala:
– \(r = 12 \) cm
– \( \theta = 120^\circ \)
Taba ea pele, re fumana bolelele ba arc:
\[P_b = \frac{\theta}{360^\circ} \times 2\pi r\]
\[P_b = \frac{120^\circ}{360^\circ} \times 2\pi \times 12\]
\[P_b = \frac{1}{3} \times 2\pi \times 12\]
\[P_b = 8\pi\mongolo{ cm}\]
Ebe re bala selikalikoe sa karolo (bolelele ba arc + radii tse peli):
\[K = 2r + P_b\]
\[K = 2 \makgetlo a 12\mongolo{cm} + 8\pi\mongolo{cm}\]
\[K = 24\mongolo{ cm} + 8\pi\mongolo{ cm}\]
Haeba \( \pi \) e nkuwa e le 3.14, joale:
\[K = 24\mongolo{cm} + 8 \makgetlo a 3.14\mongolo{cm}\]
\[K = 24\mongolo{cm} + 25.12\mongolo{cm}\]
\[K = 49.12\mongolo{cm}\]
Kahoo, sedikadikwe sohle sa lefapha lena ke 49.12 cm.
Potso ea 5:
Haeba selikalikoe se nang le radius ea 18 cm se na le karolo e etsang angle ea 45°, fumana bolelele ba arc le sebaka sa karolo eo.
Puisano:
Hoa tsebahala:
– \(r = 18 \) cm
– \( \theta = 45^\circ \)
1. Bolelele ba Arc:
\[P_b = \frac{\theta}{360^\circ} \times 2\pi r\]
\[P_b = \frac{45^\circ}{360^\circ} \times 2\pi \times 18\text{ cm}\]
\[P_b = \frac{1}{8} \times 36\pi\text{ cm}\]
\[P_b = 4.5\pi\mongolo{ cm}\]
Haeba \( \pi \) e nkuwa e le 3.14, joale:
\[P_b = 4.5 \makgetlo a 3.14\mongolo{ cm} \hoo e ka bang 14.13\mongolo{ cm}\]
Kahoo, bolelele ba seqha bo ka ba 14.13 cm.
2. Sebaka sa Lekala:
\[L_juring = \frac{\theta}{360^\circ} \times \pi \times r^2\]
\[L_juring = \frac{45^\circ}{360^\circ} \times \pi \times (18\text{ cm})^2\]
\[L_juring = \frac{1}{8} \times \pi \times 324\text{ cm}^2\]
\[L_juring = 40.5\pi\text{ cm}^2\]
Haeba \( \pi \) e nkuwa e le 3.14, joale:
\[L_juring = 40.5 \makgetlo a 3.14\mongolo{ cm}^2 \hoo e ka bang 127.17\mongolo{ cm}^2\]
Kahoo, sebaka sa lekala lena ke hoo e ka bang 127.17 cm².
Qetello
Sehloohong sena, re buisane ka mehlala e 'maloa ea mathata mabapi le likarolo tsa selikalikoe le litharollo tsa tsona. Bohlokoa ba ho utloisisa likarolo tsa selikalikoe bo ho tseba mekhoa ea motheo ea ho bala sebaka sa lekala le bolelele ba selikalikoe. Ho itloaetsa khafetsa le ho utloisisa mokhoa oa ho sebelisa mekhoa ena mefuteng e fapaneng ea mathata ho tla thusa ho ntlafatsa bokhoni ba hau ba ho rarolla mathata a tšoanang.
