Ajụjụ Ihe Nlereanya Na-atụle Gburugburu na Arcs
Okirikiri ahụ bụ ọdịdị geometric bụ isi a na-amụkarị n'ọkwa dị iche iche nke agụmakwụkwọ. Echiche a abụghị naanị ihe dị mkpa na agụmakwụkwọ kamakwa ọ na-arụ ọrụ nke ọma na ndụ kwa ụbọchị, dịka imewe ụlọ, injinia okporo ụzọ, na ọbụna nka. Isiokwu a ga-atụle ọtụtụ nsogbu atụ gbasara okirikiri na arcs, yana ngwọta ha.
Ịghọta Gburugburu na Gburugburu Gburugburu
Okirikiri bụ nchịkọta nke isi ihe niile dị n'elu ụgbọelu nke dị anya site na ebe a na-akpọ etiti okirikiri ahụ. A na-akpọ anya site na etiti okirikiri ahụ ruo ebe ọ bụla dị na okirikiri ahụ radius. Arc nke okirikiri bụ akụkụ nke gburugburu ahụ nke isi ihe abụọ dị na okirikiri ahụ gbara gburugburu.
Usoro Ndị Dị Mkpa Ị Kwesịrị Ịma
1. Gburugburu nke okirikiri (K):
\[
K = 2 \pi r
\]
ebe \(r \) bụ radius nke okirikiri ahụ na \( \pi \approx 3.14 \) ma ọ bụ \( \pi \approx \frac{22}{7} \).
2. Mpaghara Gburugburu (A):
\[
A = \pi r^2
\]
3. Ogologo Arc (s):
\[
s = \frac{\theta}{360^\circ} \times 2 \pi r
\]
ebe \( \theta \) bụ akụkụ etiti na ogo.
4. Mpaghara Ngalaba (L):
\[
L = \frac{\theta}{360^\circ} \times \pi r^2
\]
Ajụjụ na Mkparịta ụka Ihe Nlereanya
Ajụjụ nke 1: Gburugburu nke okirikiri
Ajụjụ:
Okirikiri nwere radius nke 14 cm. Gbakọọ okirikiri nke okirikiri ahụ.
Azịza:
Iji usoro maka gburugburu nke okirikiri:
\[
K = 2 \pi r
\]
Ebe \( r = 14 \) cm,
\[
K = ugboro abụọ \frac{22}{7} \oge 14 = ugboro abụọ \oge 22 \oge 2 = 88 \, \ederede{cm}
\]
Ya mere, gburugburu okirikiri ahụ bụ 88 cm.
Ajụjụ nke 2: Mpaghara Gburugburu
Ajụjụ:
E nyere okirikiri nwere dayameta nke 10 cm. Gbakọọ mpaghara nke okirikiri ahụ.
Azịza:
Nke mbụ, anyị na-achọta radius nke okirikiri ahụ:
\[
r = \frac{d}{2} = \frac{10}{2} = 5 \, \ederede{cm}
\]
Site na iji usoro mpaghara okirikiri:
\[
A = \pi r^2
\]
\[
A = \pi \oge 5^2 = \pi \oge 25 \ihe dịka 3.14 \oge 25 = 78.5 \, \ederede{cm}^2
\]
Ya mere, mpaghara gburugburu ahụ bụ 78.5 cm².
Ajụjụ nke Atọ: Ogologo nke Arc okirikiri
Ajụjụ:
Okirikiri nwere radius nke 21 cm nwere arc nke na-emepụta nkuku etiti nke 60°. Ogologo arc ahụ dị aṅaa?
Azịza:
Iji usoro ogologo arc:
\[
s = \frac{\theta}{360^\circ} \times 2 \pi r
\]
Ebe \( \theta = 60^\circ \) na \( r = 21 \, \text{cm} \),
\[
s = \frac{60^\circ}{360^\circ} \ugboro abụọ \ugboro abụọ \frac{22}{7} \ugboro 21
\]
\[
s = \frac{1}{6} \ugboro abụọ \ugboro abụọ \frac{22}{7} \ugboro abụọ
\]
\[
s = \frac{1}{6} \ugboro 132 = 22 \, \ederede{cm}
\]
Ya mere, ogologo nke arc ahụ dị 22 cm.
Ajụjụ nke 4: Mpaghara nke Ngalaba
Ajụjụ:
Gbakọọ mpaghara nke ngalaba nke okirikiri nwere akụkụ etiti nke 90° na radius nke 7 cm.
Azịza:
Iji usoro maka mpaghara nke ngalaba:
\[
L = \frac{\theta}{360^\circ} \times \pi r^2
\]
Ebe \( \theta = 90^\circ \) na \( r = 7 \, \text{cm} \),
\[
L = \frac{90^\circ}{360^\circ} \times \pi \times 7^2
\]
\[
L = \frac{1}{4} \times \pi \times 49
\]
\[
L = \frac{49 \pi}{4}
\]
\[
L \ihe dịka \frac{49 \ugboro 3.14}{4} \ihe dịka \frac{153.86}{4} \ihe dịka 38.465 \, \ederede{cm}^2
\]
Ya mere, mpaghara nke ngalaba ahụ bụ 38.465 cm².
Ajụjụ nke Ise: Njikọta nke Ajụjụ Gburugburu na Ajụjụ Mpaghara
Ajụjụ:
Okirikiri nwere okirikiri nke 44 cm. Gbakọọ mpaghara okirikiri ahụ.
Azịza:
Nke mbụ, anyị na-ahụ radius nke okirikiri ahụ site na iji usoro gburugburu:
\[
K = 2 \pi r
\]
Ebe \( K = 44 \, \ederede{cm} \),
\[
44 = ugboro abụọ \frac{22}{7} \oge r
\]
\[
44 = \frac{44}{7} \ugboro r
\]
\[
r = \frac{44 \ugboro 7}{44} = 7 \, \ederede{cm}
\]
Na-esote, gbakọọ mpaghara nke okirikiri ahụ:
\[
A = \pi r^2
\]
\[
A = \pi \oge 7^2 = \pi \oge 49 \ihe dị ka 3.14 \oge 49 \ihe dị ka 153.86 \, \ederede{cm}^2
\]
Ya mere, mpaghara gburugburu ahụ bụ 153.86 cm².
Ajụjụ nke 6: Ntụnyere n'etiti okirikiri
Ajụjụ:
Okirikiri abụọ nwere radii nke 5 cm na 10 cm n'otu n'otu. Chọpụta oke nke okirikiri na mpaghara nke okirikiri abụọ ahụ.
Azịza:
Gburugburu:
Maka okirikiri mbụ \( r_1 = 5 \, \text{cm} \):
\[
K_1 = 2 \pi r_1 = 2 \pi \ugboro 5 = 10 \pi \, \ederede{cm}
\]
Maka okirikiri nke abụọ \( r_2 = 10 \, \text{cm} \):
\[
K_2 = 2 \pi r_2 = 2 \pi \ugboro 10 = 20 \pi \, \ederede{cm}
\]
Ntụnyere gburugburu:
\[
\frac{K_1}{K_2} = \frac{10 \pi}{20 \pi} = \frac{1}{2}
\]
Obosara:
Maka okirikiri mbụ:
\[
A_1 = \pi r_1^2 = \pi \oge 5^2 = 25 \pi \, \ederede{cm}^2
\]
Maka okirikiri nke abụọ:
\[
A_2 = \pi r_2^2 = \pi \oge 10^2 = 100 \pi \, \ederede{cm}^2
\]
Ntụnyere mpaghara:
\[
\frac{A_1}{A_2} = \frac{25 \pi}{100 \pi} = \frac{1}{4}
\]
Ya mere, oke nke okirikiri nke okirikiri abụọ ahụ bụ 1:2 na oke nke mpaghara ha bụ 1:4.
Mmechi
Ịghọta echiche na usoro ndị bụ isi maka okirikiri na arcs dị oke mkpa maka idozi nsogbu dị iche iche nke geometry. Isiokwu a na-egosi ọtụtụ ihe atụ nke nsogbu na mkparịta ụka iji mee ka nghọta gị banyere ihe a sikwuo ike. Nsogbu omume na nghọta miri emi ga-enyere gị aka itinye echiche ndị a n'ọrụ n'ọtụtụ ngalaba ọmụmụ na ọnọdụ ndụ n'ezie.
