Ihe atụ nke Ajụjụ Mkparịta ụka na Circular Arcs
Na geometry, okirikiri ahụ bụ ihe osise mbara igwe nwere ọtụtụ echiche na-adọrọ mmasị ịmụ, otu n'ime ha bụ arc. Arc bụ akụkụ nke nsọtụ okirikiri nke dị n'etiti isi ihe abụọ dị na okirikiri ahụ. N'isiokwu a, anyị ga-enyocha ọtụtụ nsogbu atụ na ngwọta ha metụtara arcs.
Nghọta Dị Mkpa nke Arcs Circular
Tupu anyị agaa n'ihu n'ajụjụ ndị a, ọ dị mkpa ịghọta ụfọdụ echiche bụ isi mbụ:
1. Gburugburu:
Okirikiri bụ nchịkọta nke isi ihe niile dị n'ime ụgbọelu nke dị anya site na ebe etiti enyere.
2. Radius (Mkpịsị aka):
radius bụ anya site n'etiti okirikiri ahụ ruo ebe ọ bụla dị n'akụkụ okirikiri ahụ.
3. Dayameta:
Dayameta ahụ bụ ogologo oge kachasị ogologo site n'otu isi ihe dị n'akụkụ okirikiri ruo ebe ọzọ dị n'akụkụ nke ọzọ site n'etiti. Dayameta ahụ bụ okpukpu abụọ nke radius.
4. Ụta:
Arc bụ akụkụ nke nsọtụ okirikiri. Ọ bụrụ na isi ihe A na B dị n'ọnụ okirikiri, mgbe ahụ arc AB bụ akụkụ nke okirikiri dị n'etiti A na B.
Usoro ndị metụtara Arcs of Circles
Iji tụọ ogologo nke arc, anyị kwesịrị ịghọta ọtụtụ usoro:
1. Ogologo Arc (L):
Ogologo nke arc gburugburu bụ ogologo nke nsọtụ nke okirikiri ahụ nke gụnyere arc ahụ. Usoro a bụ:
\[
L = r \times \theta
\]
ebe \( r \) bụ radius nke okirikiri ahụ na \( \theta \) bụ akụkụ etiti na radians nke na-ejikọta arc ahụ.
2. Ogologo Arc na Ogo:
Ọ bụrụ na akụkụ etiti dị na ogo, anyị na-eji usoro a:
\[
L = \frac{\theta}{360^\circ} \times 2\pi r
\]
ebe \( \theta \) bụ akụkụ etiti na ogo.
Ajụjụ na Mkparịta ụka Ihe Nlereanya
Ajụjụ nke 1: Ịgbakọ Ogologo Arc
Ajụjụ:
Okirikiri nwere radius nke sentimita iri. Gbakọọ ogologo nke arc nke e ji akụkụ etiti nke ogo iri isii gbakọọ.
Azịza:
– Radius nke okirikiri (\( r \)) = 10 cm
– Akụkụ etiti (\( \theta \)) = 60°
Iji usoro ogologo arc na ogo:
\[
L = \frac{\theta}{360^\circ} \times 2 \pi r
\]
\[
L = \frac{60^\circ}{360^\circ} \oge 2 \pi \oge 10 \ederede{ cm}
\]
\[
L = \frac{1}{6} \ugboro 2 \pi \ugboro 10 \ederede{ cm}
\]
\[
L = \frac{20\pi}{6} \ederede{ cm}
\]
\[
L \ihe dịka 10.47 \ederede{ cm}
\]
Ya mere, ogologo nke arc dị ihe dịka 10.47 cm.
Ajụjụ nke 2: Ịchọpụta Angle Etiti site na Ogologo Arc
Ajụjụ:
E nyere okirikiri nwere radius nke 14 cm nwere ogologo arc nke 22 cm. Chọpụta akụkụ etiti nke na-ejikọta arc ahụ na ogo.
Azịza:
– Radius nke okirikiri (\( r \)) = 14 cm
– Ogologo arc (\( L \)) = 22 cm
Jiri usoro ogologo arc chọta \( \theta \):
\[
L = \frac{\theta}{360^\circ} \times 2 \pi r
\]
Dochie ụkpụrụ ndị a maara:
\[
22 = \frac{\theta}{360^\circ} \oge 2 \pi \oge 14
\]
Nnọpụiche \( \theta \):
\[
22 = \frac{\theta}{360^\circ} \times 28 \pi
\]
\[
22 \ugboro 360^\cir = \theta \ugboro 28 \pi
\]
\[
7920 = \theta \times 28 \pi
\]
\[
\theta = \frac{7920}{28 \pi}
\]
\[
\theta \ihe dịka 90.72^\gburugburu
\]
Ya mere, nha nke akụkụ etiti dị ihe dịka ogo 90.72.
Ajụjụ nke 3: Ịgbakọ Mpaghara nke Ngalaba
Ajụjụ:
A na-eji akụkụ etiti nke ogo 120 na radius nke 7 cm mepụta ngalaba nke okirikiri. Chọpụta mpaghara nke ngalaba ahụ.
Azịza:
– Radius nke okirikiri (\( r \)) = 7 cm
– Akụkụ etiti (\( \theta \)) = 120°
Jiri usoro maka mpaghara nke ngalaba:
\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]
Dochie ụkpụrụ ndị a maara:
\[
A = \frac{120^\circ}{360^\circ} \times \pi \times 7^2
\]
\[
A = \frac{1}{3} \times \pi \times 49
\]
\[
A = \frac{49\pi}{3}
\]
\[
A \ihe dị ka 51.43 \ederede{ cm}^2
\]
Ya mere, mpaghara nke ngalaba ahụ dị ihe dịka 51.43 cm².
Ajụjụ nke 4: Ịchọpụta Arc site na Mpaghara nke Ngalaba
Ajụjụ:
Mpaghara nke ngalaba okirikiri nwere radius nke 6 cm bụ 18π cm². Ogologo nke arc nke ngalaba ahụ dị aṅaa?
Azịza:
– Radius nke okirikiri (\( r \)) = 6 cm
– Mpaghara nke ngalaba (\( A \)) = 18π cm²
Jiri usoro mpaghara maka ngalaba iji chọta akụkụ etiti \( \theta \):
\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]
Dochie ụkpụrụ ndị a maara:
\[
18\pi = \frac{\theta}{360^\circ} \times \pi \times 6^2
\]
\[
18\pi = \frac{\theta}{360^\circ} \times 36\pi
\]
\[
18 = \frac{\theta}{360^\circ} \ugboro 36
\]
\[
18 \ugboro 360^\cir = \theta \ugboro 36
\]
\[
6480 = \theta \oge 36
\]
\[
\theta = \frac{6480}{36}
\]
\[
\theta = 180^\gburugburu
\]
Ugbua, site na nkuku etiti nke ogo 180, anyị na-ekpebi ogologo arc:
\[
L = \frac{\theta}{360^\circ} \times 2 \pi r
\]
\[
L = \frac{180^\circ}{360^\circ} \ugboro 2 \pi \ugboro 6
\]
\[
L = \frac{1}{2} \ugboro 2 \pi \ugboro 6
\]
\[
L = \pi \ugboro 6
\]
\[
L \ihe dịka 18.85 \ederede{ cm}
\]
Ya mere, ogologo ụta ahụ dị ihe dị ka 18.85 cm.
Mmechi
Ịghọta arcs gburugburu na otu esi agbakọ ha bụ ntọala dị mkpa na geometry na mgbakọ na mwepụ n'ozuzu. Site na ihe atụ ndị a tụlere n'isiokwu a, a na-atụ anya ka ndị na-agụ akwụkwọ ghọta nke ọma otu esi agbakọ ogologo arc, mpaghara ngalaba, na ịchọpụta akụkụ etiti nke na-ejikọ arc. Nghọta dị mma nke echiche ndị a bụ isi ga-enyere aka nke ukwuu n'idozi nsogbu dị iche iche metụtara okirikiri.
