Te Tātai i te Horahanga Mata o te Porowhita
Ko te porowhita tētahi o ngā āhua ā-ira tino kitea i roto i te ao o ia rā. Ka kitea tōna āhua i roto i ngā momo taonga, mai i ngā pōro whutupaoro me ngā māpere ki ngā poitūkohu me ngā aorangi me ngā whetu. I roto i te pāngarau, he āhuatanga ahurei tō te porowhita nā te mea he ōrite te tawhiti o ngā pūwāhi katoa i runga i tōna mata mai i tētahi pūwāhi pokapū kotahi. Ko tētahi kaupapa nui e akohia ana mō ngā porowhita ko te horahanga o te mata. Ko te mārama ki te tatau i a ia ehara i te mea he mea whai hua mō ngā kaupapa kura anake engari he mea whai hua anō hoki mō ngā momo mara pērā i te hangarau, te ahupūngao, te hoahoanga, tae atu ki te hoahoa hua.
Te mārama ki te porowhita me tōna mata
I mua i te urunga atu ki te tātai, me mārama tātou ki te horahanga o te mata o te porowhita. Ko te horahanga o te mata o te porowhita ko te anga o waho e karapoti ana i te porowhita katoa. Mena ka taea te "tapahia" me te "toro" i te porowhita (ahakoa he uaua tēnei), ko te anga o waho te mea e hiahia ana tātou ki te tatau i te horahanga.
He maha ngā āhuatanga nui o te pōro, tae atu ki:
1. Pūwāhi pokapū: te pūwāhi i waenganui o te pōro.
2. Pūtoro (r): te tawhiti mai i te pūwāhi pokapū ki te mata o te pōro.
3. Te whānui (d): te tawhiti roa rawa atu e tika ana mā waenganui o te pōro, ko tōna uara he rua te rahi o te pūtoro (d = 2r).
I te tatau i te horahanga o te mata o te porowhita, ko te uara e whakamahia pinepinetia ana ko te radius.
Te tātai horahanga mata mō te porowhita
Ko te tātai mō te horahanga o te mata o te porowhita ko:
L = 4πr²
Ngā Mōhiohio:
– L = horahanga mata o te pōro
– π (pi) = pūmau tata ki te 3,14159 (he maha ngā wā ka whakaawhiwhia ki te 3,14, ki te 22/7 rānei)
– r = te pūtoro o te pōro
E whakaatu ana tēnei tātai ko te horahanga o te mata o te porowhita e whakawhirinaki ana ki te tapawhā o te pūtoro. Ko te tikanga, ki te takiruahia te pūtoro o te porowhita, ka whā te horahanga o tōna mata. Nā te huānga r² i roto i te tātai tēnei.
He aha i 4πr² ai te tātai?
I te kura, ka hoatuhia tēnei tauira hei tauira kua oti te hanga. Heoi, he māmā ake te maumahara me te whakamahi mēnā ka mārama tātou ki te ariā taketake. I roto i te ariā, he whanaungatanga kei waenganui i te porowhita me te porowhita.
Ko te horahanga o te porowhita he πr². He mea whakamīharo, ko te horahanga o te mata o te porowhita he whā ngā wā o te horahanga o tētahi porowhita nui ake (he porowhita he rite te radius ki te porowhita). Nō reira:
Te horahanga o te mata o te porowhita = 4 × (te horahanga o te porowhita)
= 4 × πr²
= 4πr²
Ka taea te mārama ki tēnei whanaungatanga "whā" mā roto i ngā huarahi ā-ira me ngā huarahi whakamātautau (hei tauira, te whakatairite i te horahanga o te mata o te porowhita ki te horahanga o te mata o tētahi rango), ahakoa ko tōna taunakitanga ōkawa ka akohia i te taumata teitei ake.
Ngā taahiraa hei tatau i te horahanga mata o te porowhita
Hei whakapūmau ake i te pūnaha, anei ngā mahi whānui mō te tatau i te horahanga o te mata o te porowhita:
1. Tāutuhia te radius o te pōro (r)
Ki te mōhiotia te whānui, ko r = d/2.
2. Whakamahia te tātai L = 4πr²
Monohia te uara r ki roto i te tātai.
3. Kōwhiria te uara tika o π
– Whakamahia te π = 3,14 mō ngā tātaitanga mahi.
– Whakamahia te π = 22/7 mēnā he tauwehenga 7 a r mō ngā hua māmā ake.
4. Tātaihia te r², kātahi ka whakareatia ki te 4π
Kia tino tika te whakahaere i ngā mahi tātai.
5. Tuhia ngā waeine o te horahanga
Mena kei roto i te cm te r, ko te horahanga kei roto i te cm²; mena kei roto i te mita te r, ko te horahanga kei roto i te m², ā, pērā tonu.
Tauira pātai 1: te pūtoro e mōhiotia ana
Pātai: He 7 cm te whānui o te porowhita. Tātaihia tōna horahanga mata.
Otinga:
– r = 7 henimita
– L = 4πr²
– R = 4 × (22/7) × 7²
– L = 4 × (22/7) × 49
– L = 4 × 22 × 7
– R = 616 henimita²
Nō reira, ko te horahanga o te mata o te pōro he 616 cm².
Tauira pātai 2: i te mea kua hoatu te diameter
Pātai: Ko te whānui o te pōro he 20 cm. He aha te horahanga o tōna mata?
Otinga:
– d = 20 henemita
– r = d/2 = 10 cm
– L = 4πr²
– R = 4 × 3,14 × 10²
– L = 4 × 3,14 × 100
– R = 1256 henimita²
Nō reira, ko te horahanga o te mata o te porowhita he 1256 cm².
Ngā hapa noa hei karo
I te tatau i te horahanga o te mata o te porowhita, ko ētahi hapa ka puta pinepine ko:
1. Te hē o te mārama ki te pūtoro me te whānui
He tokomaha te hunga e whakauru noa ana i te diameter ki roto i te tātai me te mea ko te radius. Heoi, e whakamahia ana e te tātai te r, ehara i te d.
2. I wareware ki te tapawhā i te pūtoro
Ko te tātai ko r², ehara i te r. Nō reira, ki te mea ko r = 10, ko r² = 100, ehara i te 10.
3. Ngā waeine kore taurite
Hei tauira, mēnā kei roto i te cm te pūtoro, engari ko te hua ka tuhia hei m², me whakarite kei te tika ngā waeine mai i te tīmatanga.
4. Kōwhiringa hē o π
He pai te whakamahi i te 3,14, i te 22/7 rānei, engari whakamahia kia tika ai te whakamahi. Mēnā ehara a r i te tauwehenga o te 7, mā te whakamahi i te 22/7 ka hua ake he hautau uaua ake.
Te whakamahinga o te horahanga mata o te porowhita i te ao tūturu
Ehara i te mea he mahi pāngarau noa te tatau i te horahanga o te mata o te porowhita. E whakamahia ana tēnei ariā i roto i ngā āhuatanga maha, hei tauira:
– Tātaihia te hiahia mō te peita, te paninga rānei mō ngā mea porowhita, pērā i ngā whakapaipai porowhita nui, ngā tāke porowhita rānei.
– Ngā tātaitanga i roto i te ahupūngao, pērā i te horahanga o te mata o tētahi aorangi hei whakatau tata i te irahiko o te rā e whiwhihia ana, e tukuna ana rānei.
– Te hoahoa hua, hei tauira, te whakatau i te horahanga o te rauemi hei hanga pōro kirihou, pōro rapa rānei.
– Te arorangi whetū, hei tauira, te tatau i te horahanga o te mata o ngā whetū, o ngā aorangi rānei hei tātari i te pāmahana me te pūngao.
Ka nui ake te porowhita, ka nui ake tōna horahanga mata, ā, e whai ana tēnei whanaungatanga i te tātai 4πr². Nō reira, mā te iti o te huringa o te radius ka hua ake he huringa nui o te horahanga.
Te Katinga
Ko te horahanga o te mata o te porowhita ko te horahanga katoa o te anga o waho o te porowhita. Hei tatau, ka whakamahia e mātou te tātai L = 4πr², ko r te pūtoro o te porowhita. Ko te mea nui ki te tatau tika ko te whakarite kia tika te pūtoro (ina koa mēnā kua hoatu te whānui), kia tupato ki te tapawhā i te r, te whiriwhiri i te uara tika o te π, me te tuhi tika i ngā waeine horahanga.
Mā te mārama ki ngā mahi me ngā tauira, ka māmā ake te tatau i te horahanga o te mata o te porowhita. Hei whakamutunga, ka taea te whakamahi i tēnei pūkenga ehara i te mea ki ngā raruraru pāngarau anake engari ki ngā raruraru o te ao tūturu e pā ana ki ngā mea porowhita e karapoti nei i a tātou.
