Nā nīnau hoʻohālike e kūkākūkā ana i nā pōʻai a me nā piʻo
He ʻano geometric kumu ka pōʻai i aʻo pinepine ʻia ma nā pae hoʻonaʻauao like ʻole. ʻAʻole pili wale kēia manaʻo i ka ʻoihana kula akā he nui nā noi i ke ola o kēlā me kēia lā, e like me ka hoʻolālā kuhikuhipuʻuone, ka ʻenekinia alanui, a me ke kiʻi. E kūkākūkā kēia ʻatikala i nā pilikia hoʻohālike like ʻole e pili ana i nā pōʻai a me nā piʻo, me kā lākou mau hoʻonā.
Ke Hoʻomaopopo ʻana i nā Pōʻai a me nā Piʻo Pōʻai
ʻO ka pōʻai ka hōʻiliʻili ʻana o nā kiko āpau ma kahi mokulele e like ka mamao mai kahi kiko i kapa ʻia ʻo ke kikowaena o ka pōʻai. ʻO ka mamao mai ke kikowaena o ka pōʻai a i kekahi kiko ma ka pōʻai ua kapa ʻia ʻo ka radius. ʻO ka piʻo o ka pōʻai ka ʻāpana o ke anapuni i hoʻopuni ʻia e ʻelua mau kiko ma ka pōʻai.
Nā Haʻilula Kumu e Pono ai ʻoe e ʻIke
1. Kaapuni o kahi Pōʻai (K):
\[
K = 2 \pi r
\]
kahi ʻo \( r \) ke radius o ka pōʻai a me \( \pi \approx 3.14 \) a i ʻole \( \pi \approx \frac{22}{7} \).
2. ʻĀpana o ka Pōʻai (A):
\[
A = \pi r^2
\]
3. Ka Lōʻihi o ke ʻĀkau (s):
\[
s = \frac{\theta}{360^\circ} \times 2 \pi r
\]
kahi ʻo \( \theta \) ke kihi kikowaena ma nā kekelē.
4. ʻĀpana ʻĀpana (L):
\[
L = \frac{\theta}{360^\circ} \times \pi r^2
\]
Nā Nīnau Laʻana a me ke Kūkākūkā
Nīnau 1: Ka Pōʻai o kahi Pōʻai
Nīnau:
He 14 kenimika ka radius o kahi pōʻai. E helu i ke anapuni o ka pōʻai.
Kūkākūkā:
Ke hoʻohana nei i ke ʻano no ka anapuni o kahi pōʻai:
\[
K = 2 \pi r
\]
Ma kahi o \( r = 14 \) kenimika,
\[
K = 2 \times \frac{22}{7} \times 14 = 2 \times 22 \times 2 = 88 \, \text{cm}
\]
No laila, ʻo ke anapuni o ka pōʻai he 88 kenimika.
Nīnau 2: Ka ʻĀpana o kahi Pōʻai
Nīnau:
Hāʻawi ʻia kahi pōʻai me ke anawaena o 10 kenimika. E helu i ka ʻāpana o ka pōʻai.
Kūkākūkā:
ʻO ka mea mua, ʻike mākou i ka radius o ka pōʻai:
\[
r = \frac{d}{2} = \frac{10}{2} = 5 \, \text{cm}
\]
Ke hoʻohana nei i ke ʻano hana o ka ʻāpana pōʻai:
\[
A = \pi r^2
\]
\[
A = \pi \times 5^2 = \pi \times 25 \approx 3.14 \times 25 = 78.5 \, \text{cm}^2
\]
No laila, ʻo ka nui o ka pōʻai he 78.5 cm².
Nīnau 3: Ka lōʻihi o kahi ʻāʻī poepoe
Nīnau:
He pōʻai me ka radius o 21 kenimika he piʻo e hana ana i kahi kihi waena o 60°. He aha ka lōʻihi o ke piʻo?
Kūkākūkā:
Ke hoʻohana nei i ke ʻano o ka lōʻihi o ke arc:
\[
s = \frac{\theta}{360^\circ} \times 2 \pi r
\]
Ma kahi o \( \theta = 60^\circ \) a me \( r = 21 \, \text{cm} \),
\[
s = \frac{60^\circ}{360^\circ} \times 2 \times \frac{22}{7} \times 21
\]
\[
s = \frac{1}{6} \times 2 \times \frac{22}{7} \times 21
\]
\[
s = \frac{1}{6} \times 132 = 22 \, \text{cm}
\]
No laila, ʻo ka lōʻihi o ke ana he 22 kenimika.
Nīnau 4: ʻĀpana o kahi ʻĀpana
Nīnau:
E helu i ka ʻāpana o kahi ʻāpana o ka pōʻai nona ke kihi kikowaena o 90° a me ka radius o 7 kenimika.
Kūkākūkā:
Ke hoʻohana nei i ke ʻano no ka ʻāpana o kahi ʻāpana:
\[
L = \frac{\theta}{360^\circ} \times \pi r^2
\]
Ma kahi o \( \theta = 90^\circ \) a me \( r = 7 \, \text{cm} \),
\[
L = \frac{90^\circ}{360^\circ} \times \pi \times 7^2
\]
\[
L = \frac{1}{4} \times \pi \times 49
\]
\[
L = \frac{49 \pi}{4}
\]
\[
L \approx \frac{49 \times 3.14}{4} \approx \frac{153.86}{4} \approx 38.465 \, \text{cm}^2
\]
No laila, ʻo ka ʻāpana o ka ʻāpana he 38.465 cm².
Nīnau 5: Hui Pū ʻana o nā Nīnau Kaapuni a me ka ʻĀpana
Nīnau:
He 44 kenimika ka anapuni o kahi pōʻai. E helu i ka nui o ka pōʻai.
Kūkākūkā:
ʻO ka mea mua, ʻike mākou i ka radius o ka pōʻai me ka hoʻohana ʻana i ke ʻano circumference:
\[
K = 2 \pi r
\]
Ma kahi o \( K = 44 \, \text{cm} \),
\[
44 = 2 manawa \frac{22}{7} manawa r
\]
\[
44 = \frac{44}{7} \times r
\]
\[
r = \frac{44 \times 7}{44} = 7 \, \text{cm}
\]
A laila, e helu i ka ʻāpana o ka pōʻai:
\[
A = \pi r^2
\]
\[
A = \pi \times 7^2 = \pi \times 49 \approx 3.14 \times 49 \approx 153.86 \, \text{cm}^2
\]
No laila, ʻo ka nui o ka pōʻai he 153.86 cm².
Nīnau 6: Hoʻohālikelike ma waena o nā Pōʻai
Nīnau:
He 5 kenimika a he 10 kenimika nā radius o nā pōʻai ʻelua. E hoʻoholo i ka lakio o ke anapuni a me ka laulā o nā pōʻai ʻelua.
Kūkākūkā:
A puni:
No ka pōʻai mua \( r_1 = 5 \, \text{cm} \):
\[
K_1 = 2 \pi r_1 = 2 \pi \times 5 = 10 \pi \, \text{cm}
\]
No ka pōʻai ʻelua \( r_2 = 10 \, \text{cm} \):
\[
K_2 = 2 \pi r_2 = 2 \pi \times 10 = 20 \pi \, \text{cm}
\]
Hoʻohālikelike ʻana o ka palena:
\[
\frac{K_1}{K_2} = \frac{10 \pi}{20 \pi} = \frac{1}{2}
\]
Laulā:
No ka pōʻai mua:
\[
A_1 = \pi r_1^2 = \pi \times 5^2 = 25 \pi \, \text{cm}^2
\]
No ka lua o ka pōʻai:
\[
A_2 = \pi r_2^2 = \pi \times 10^2 = 100 \pi \, \text{cm}^2
\]
Hoʻohālikelike ʻāpana:
\[
\frac{A_1}{A_2} = \frac{25 \pi}{100 \pi} = \frac{1}{4}
\]
No laila, ʻo ka lakio o nā anapuni o nā pōʻai ʻelua he 1:2 a ʻo ka lakio o ko lākou ʻāpana he 1:4.
Ka hopena
He mea nui ka hoʻomaopopo ʻana i nā manaʻo kumu a me nā ʻano hana no nā pōʻai a me nā ʻāʻī no ka hoʻoponopono ʻana i nā pilikia geometry like ʻole. Hōʻike kēia ʻatikala i kekahi mau pilikia hoʻohālike a me nā kūkākūkā e hoʻoikaika i kou ʻike i kēia mea. E kōkua nā pilikia hoʻomaʻamaʻa a me ka hoʻomaopopo hohonu iā ʻoe e hoʻopili i kēia mau manaʻo ma nā ʻano like ʻole o ke aʻo ʻana a me nā kūlana ola maoli.
