Ke Helu ʻana i ka Leo o kahi Prism: He Alakaʻi Piha
ʻO nā prisms kekahi o nā kinona geometric a mākou e ʻike pinepine ai i ke ola o kēlā me kēia lā. Inā paha ma nā kinona maʻalahi e like me nā pahu a i ʻole nā kinona paʻakikī e like me nā prisms hexagonal, ʻo ke kumumanaʻo kumu no ka helu ʻana i ka nui o kahi prism ua like like. Ma kēia ʻatikala, e nānā pono mākou i ke ʻano o ka helu ʻana i ka nui o kahi prism, me ka wehewehe ʻana, nā waiwai, nā ʻano o nā prism, nā ʻano helu, a me nā laʻana maoli.
1. He aha ka Prism?
He kiʻi geometric ʻekolu-dimensional ka prism me ʻelua mau kumu like, like a me nā ʻaoʻao huinahā. Hoʻohana pinepine ʻia nā prism ma muli o ke ʻano o ko lākou mau kumu; no ka laʻana, he kumu huinakolu ko ka prism triangular, a he kumu huinahā a huinahā paha ko ka prism rectangular a i ʻole cube.
Nā ʻano o nā Prisms:
1. Loaʻa iā ia ʻelua mau kumu e kūlike a like hoʻi.
2. Kū pololei a ʻehā paha nā ʻaoʻao.
3. ʻO kēlā me kēia ʻāpana kea e kūlike ana i ke kumu ua kūlike ia me ke kumu.
2. Nā ʻAno o nā Prisms
Hiki ke hoʻokaʻawale ʻia nā prisma ma muli o ke ʻano o ko lākou kumu:
– ʻO ka Prism Triangular: He triangular ke kumu. He ʻekolu ona ʻaoʻao huinahā.
– ʻO ka Prism Quadrilateral (Cube a i ʻole Cuboid): He huinahā a he ʻāpana huinahā paha ke kumu. Loaʻa i nā cubes nā ʻaoʻao o ka lōʻihi like, ʻoiai he ʻokoʻa ka lōʻihi a me ka laulā o nā cuboids.
– Pentagonal Prism: He pentagonal ke kumu. He ʻelima ona ʻaoʻao huinahā.
– ʻO ka Prism Hexagonal: He hexagon ke kumu. He ʻeono ona helehelena huinahā.
3. Formula no ka helu ʻana i ka nui o ka Prism
Ua helu ʻia ka nui o ka prism me ka hoʻohana ʻana i ke ʻano hana:
\[ \text{Volume} = \text{ʻĀpana o ke Kumu} \times \text{Kiʻekiʻe o ka Prism} \]
ʻO ke kī i ka helu ʻana i ka leo ka hoʻoholo ʻana i ka ʻāpana o ke kumu a me ke kiʻekiʻe o ka prism.
Nā hiʻohiʻona o nā helu ʻana ma nā ʻano prism like ʻole:
– ʻO ka Prism Triangular:
Manaʻo ʻia he huinakolu ke kumu me ke kumu \(a \) a me ke kiʻekiʻe \(t \), a ʻo ke kiʻekiʻe o ka prism ʻo \(h \).
ʻĀpana o ke kumu o kahi prism triangular:
\[ L = \frac{1}{2} \times a \times t \]
Ka nui o ka prism huinakolu:
\[ V = L \times h = \frac{1}{2} \times a \times t \times h \]
– ʻO ka Prism ʻaoʻao ʻehā (Cuboid):
Manaʻo ʻia he huinahā ke kumu me ka lōʻihi \(p \) a me ka laulā \(l \), a me ke kiʻekiʻe o ka prism \(h \).
ʻĀpana o ke kumu o kahi prism huinahā:
\[ L = p \times l \]
Ka nui o kahi prism huinahā (cube):
\[ V = L \times h = p \times l \times h \]
– Nā Prisms Pentagonal a me Hexagonal:
No kahi prism me kahi kumu pentagonal a hexagonal paha, ka helu ʻana o ka ʻāpana Hiki i ke kumu ke hoʻohana i kahi ʻano kūikawā no kēlā me kēia o kēia mau ʻano mokulele. No ka laʻana, no kahi hexagon maʻamau me ka lōʻihi o ka ʻaoʻao \( s \):
\[ L = \frac{3\sqrt{3}}{2} \times s^2 \]
Me ke kiʻekiʻe o ka prism \( h \):
Ka nui o ka prism hexagonal:
\[ V = L \times h = \frac{3\sqrt{3}}{2} \times s^2 \times h \]
4. Laʻana o ka Hihia o ka Helu ʻana i ka Leo o kahi Prism
Laʻana 1: ʻO ka Prism Triangular
He 6 kenimika ka lōʻihi o ke kumu o kahi prism triangular, 4 kenimika ke kiʻekiʻe, a he 10 kenimika ke kiʻekiʻe. E helu i ka nui o ka prism.
Wahi kumu:
\[ L = \frac{1}{2} \times 6 \times 4 = 12 \, \text{cm}^2 \]
Ka nui o ka prism:
\[ V = L \times h = 12 \times 10 = 120 \, \text{cm}^3 \]
Laʻana 2: Poloka
He 5 m ka lōʻihi o kahi poloka, 3 m ka laulā, a he 2 m ke kiʻekiʻe. E helu i ka nui o kahi cuboid kēlā.
Wahi kumu:
\[ L = 5 \times 3 = 15 \, \text{m}^2 \]
Ka nui o kahi cuboid:
\[ V = L \times h = 15 \times 2 = 30 \, \text{m}^3 \]
Laʻana 3: ʻŌlinolino Hexagonal
He 2 kenimika ka lōʻihi o ka ʻaoʻao kumu o kahi prism hexagonal maʻamau a he 12 kenimika ke kiʻekiʻe. E helu i ka nui o ka prism.
Wahi kumu:
\[ L = \frac{3\sqrt{3}}{2} \times 2^2 = 6\sqrt{3} \, \text{cm}^2 \]
Ka nui o ka prism:
\[ V = L \times h = 6\sqrt{3} \times 12 = 72\sqrt{3} \, \text{cm}^3 \]
5. Hoʻopili ʻana ma ke ola maoli
ʻAʻole wale ka helu ʻana i ka nui o ka prism he hana makemakika ma ke kula; he nui nā noi kūpono. Eia kekahi laʻana:
– Kuhikuhipuʻuone a me ke Kūkulu ʻana: Hoʻohana pinepine nā ʻenekinia i ka manaʻo o ka nui o ka prism e hoʻoholo ai i nā mea kūkulu hale e pono ai, e like me ka sima.
– Hoʻolālā Huahana: Ua hoʻolālā ʻia nā huahana he nui, e like me nā pahu hoʻopili, ma muli o ke kumumanaʻo o ka nui prism no ka pono o ka wahi.
– Ka Halihali a me ka Logistics: Hoʻohana ʻia ka nui o kahi prism e helu ai i ka ukana e hiki ke hoʻokipa ʻia i loko o kahi kalaka a i ʻole ka ipu.
6. Manaʻo
ʻO nā prisms kekahi o nā kinona geometric kumu koʻikoʻi loa i ka makemakika a he mau noi ākea ko lākou i ke ao maoli. ʻO ka hoʻomaopopo ʻana i ke ʻano a me pehea e helu ai i ka nui o kahi prism hiki ke maʻalahi i ka hoʻoponopono ʻana i nā pilikia hana like ʻole. ʻO ke ʻano nui o ka nui, ʻo ia ka hoʻonui ʻana i ka ʻāpana o ke kumu me ke kiʻekiʻe o ka prism. ʻO ka hoʻopili ʻana i kēia ʻano e pono ai ka pololei i ka hoʻoholo ʻana i ka ʻāpana o ke kumu e pili ana i kona ʻano a me ke kiʻekiʻe o ka prism. Me ka lawa ʻana o ka hoʻomaʻamaʻa, e lilo ka helu ʻana i ka nui o kahi prism i mākaukau pono loa.
