Ajụjụ na Mkparịta ụka Ihe Nlereanya nke Ngalaba Gburugburu
Ngalaba nke okirikiri bụ isiokwu dị mkpa na mgbakọ na mwepụ nke na-apụtakarị n'ajụjụ ule na omume. Ngalaba bụ akụkụ nke okirikiri nke nwere radii abụọ na arc na-ejikọ ha. N'isiokwu a, anyị ga-atụle ọtụtụ nsogbu atụ na ngalaba nke okirikiri, yana nkọwa zuru ezu, iji mee ka nghọta anyị dịkwuo omimi.
Nkọwa nke Ngalaba Gburugburu
Ngalaba nke okirikiri bụ ngalaba nke okirikiri nke ejiri radii abụọ na otu arc kewaa. A na-agbakọ mpaghara nke ngalaba dabere na obere akụkụ nke mpaghara okirikiri ahụ dum. Usoro bụ isi eji agbakọ ngalaba bụ dị ka ndị a:
– Mpaghara Juring: \[L_juring = \frac{\theta}{360^\circ} \times \pi \times r^2\]
– Ogologo Arc: \[P_b = \frac{\theta}{360^\circ} \times 2\pi r\]
Ebe:
– \( \theta \) bụ nha nke akụkụ ngalaba na ogo,
– \( r \) bụ radius nke okirikiri ahụ,
– \( \pi \) bụ ihe na-agbanweghi agbanwe (ihe dị ka 3.14159).
Ajụjụ na Mkparịta ụka Ihe Nlereanya
Ajụjụ nke Mbụ:
E nyere okirikiri nwere radius nke 10 cm na ngalaba nwere akụkụ etiti nke 90°. Gbakọọ mpaghara nke ngalaba ahụ.
Azịza:
A maara:
– \( r = 10 \) cm
– \( \theta = 90^\cir \)
Anyị na-eji usoro maka mpaghara nke ngalaba:
\[L_juring = \frac{\theta}{360^\circ} \times \pi \times r^2\]
\[L_juring = \frac{90^\circ}{360^\circ} \times \pi \times (10\text{ cm})^2\]
\[L_juring = \frac{1}{4} \times \pi \times 100\text{ cm}^2\]
\[L_juring = 25\pi\text{ cm}^2\]
Ọ bụrụ na a na-ewere \( \pi \) dị ka 3.14, mgbe ahụ:
\[L_juring = 25 \ugboro 3.14\ederede{ cm}^2 = 78.5\ederede{ cm}^2\]
Ya mere, mpaghara nke ngalaba ahụ bụ 78.5 cm².
Ajụjụ nke Mbụ:
Ngalaba okirikiri nwere radius nke 7 cm na ogologo arc nke 11 cm. Chọpụta akụkụ etiti nke ngalaba ahụ na radians.
Azịza:
A maara:
– \( r = 7 \) cm
– Ogologo Arc \( P_b = 11 \ederede{ cm} \)
Anyị na-eji usoro ogologo arc iji chọta akụkụ \( \theta \):
\[P_b = \frac{\theta}{360^\circ} \times 2\pi r\]
Ebe ọ bụ na a gwara anyị ka anyị chọta akụkụ dị na radians, anyị na-eji radians \(2\pi\) dochie 360°:
\[P_b = \theta \times r\]
\[11 = \theta \times 7\]
\[\theta = \frac{11}{7}\]
\[\theta \ihe dịka 1.57 \text{ rad}\]
Ya mere, akụkụ etiti nke ngalaba ahụ bụ 1.57 radians.
Ajụjụ nke Mbụ:
Okirikiri nwere radius nke 16 cm nwere ngalaba nwere mpaghara nke 200 cm². Gbakọọ akụkụ etiti nke ngalaba ahụ.
Azịza:
A maara:
– \( r = 16 \) cm
– \( L_juring = 200 \ederede{ cm}^2 \)
Anyị na-eji usoro mpaghara maka ngalaba iji chọta \( \theta \):
\[L_juring = \frac{\theta}{360^\circ} \times \pi \times r^2\]
\[200 = \frac{\theta}{360^\circ} \times \pi \times (16)^2\]
\[200 = \frac{\theta}{360^\circ} \times \pi \times 256\]
\[200 = \frac{\theta \times 256 \times \pi}{360^\circ}\]
\[200 \ugboro 360^\circ = \theta \ugboro 256 \ugboro 3.14\]
\[72000 = \theta \oge 256 \oge 3.14\]
\[72000 = \theta \times 804.64\]
\[\theta = \frac{72000}{804.64}\]
\[\theta \ihe dịka 89.45^\circ\]
Ya mere, akụkụ etiti nke ngalaba ahụ bụ ihe dịka 89.45°.
Ajụjụ nke Mbụ:
Gbakọọ gburugburu nke ngalaba nwere radius nke 12 cm na akụkụ etiti nke 120 °.
Azịza:
A maara:
– \( r = 12 \) cm
– \( \theta = 120^\cir \)
Nke mbụ, anyị na-achọta ogologo arc:
\[P_b = \frac{\theta}{360^\circ} \times 2\pi r\]
\[P_b = \frac{120^\circ}{360^\circ} \ugboro 2\pi \ugboro 12\]
\[P_b = \frac{1}{3} \ugboro 2\pi \ugboro 12\]
\[P_b = 8\pi\ederede{ cm}\]
Mgbe ahụ, anyị na-agbakọ gburugburu nke ngalaba ahụ (ogologo arc + radii abụọ):
\[K = 2r + P_b\]
\[K = ugboro abụọ 12\ederede{ cm} + 8\pi\ederede{ cm}\]
\[K = 24\ederede{ cm} + 8\pi\ederede{ cm}\]
Ọ bụrụ na a na-ewere \( \pi \) dị ka 3.14, mgbe ahụ:
\[K = 24\ederede{ cm} + 8 \ugboro 3.14\ederede{ cm}\]
\[K = 24\ederede{ cm} + 25.12\ederede{ cm}\]
\[K = 49.12\ederede{ cm}\]
Ya mere, gburugburu mpaghara ahụ dum bụ 49.12 cm.
Ajụjụ nke Mbụ:
Ọ bụrụ na okirikiri nwere radius nke 18 cm nwere ngalaba nke na-eme nkuku nke 45°, chọpụta ogologo nke arc na mpaghara nke ngalaba ahụ.
Azịza:
A maara:
– \( r = 18 \) cm
– \( \theta = 45^\cir \)
1. Ogologo Arc:
\[P_b = \frac{\theta}{360^\circ} \times 2\pi r\]
\[P_b = \frac{45^\circ}{360^\circ} \times 2\pi \times 18\text{ cm}\]
\[P_b = \frac{1}{8} \ugboro 36\pi\text{ cm}\]
\[P_b = 4.5\pi\ederede{ cm}\]
Ọ bụrụ na a na-ewere \( \pi \) dị ka 3.14, mgbe ahụ:
\[P_b = 4.5 \ugboro 3.14\ederede{ cm} \ihe dịka 14.13\ederede{ cm}\]
Ya mere, ogologo ụta ahụ dị ihe dị ka 14.13 cm.
2. Mpaghara nke ngalaba:
\[L_juring = \frac{\theta}{360^\circ} \times \pi \times r^2\]
\[L_juring = \frac{45^\circ}{360^\circ} \times \pi \times (18\text{ cm})^2\]
\[L_juring = \frac{1}{8} \times \pi \times 324\text{ cm}^2\]
\[L_juring = 40.5\pi\text{ cm}^2\]
Ọ bụrụ na a na-ewere \( \pi \) dị ka 3.14, mgbe ahụ:
\[L_juring = 40.5 \ugboro 3.14\ederede{ cm}^2 \ihe dịka 127.17\ederede{ cm}^2\]
Ya mere, mpaghara nke ngalaba ahụ dị ihe dịka 127.17 cm².
Mmechi
N'isiokwu a, anyị atụleela ọtụtụ ihe atụ gbasara ngalaba nke okirikiri na ngwọta ha. Isi ihe dị mkpa nke ịghọta ngalaba nke okirikiri dị n'ịmụta usoro ndị bụ isi maka ịgbakọ mpaghara nke ngalaba na ogologo nke arc. Ịmụ ihe mgbe niile na ịghọta otu esi etinye usoro ndị a n'ọtụtụ ụdị nsogbu ga-enyere aka melite ikike gị idozi nsogbu ndị yiri ya.
