Me pēhea te tatau i te rōrahi o te poraka
Ko te poraka tētahi o ngā āhua ā-ira tino kitea i roto i te pāngarau. He ōrite te āhua, he ōrite ngā taha katoa, ā, he maha tonu ngā wā ka tūtaki tātou ki tēnei āhua i roto i te ao o ia rā—mai i ngā mataono ki ngā pouaka koha āhua-poraka ki ngā momo hoahoa rokiroki. Ko tētahi o ngā kaupapa matua hei mārama i te wā e ako ana i ngā poraka ko te tatau i tō rātou rōrahi. Ko te rōrahi o te poraka e tohu ana i te nui o te wāhi ka taea e te poraka te pupuri. Ka matapakihia e tēnei tuhinga te whakamāramatanga o te rōrahi, te tātai mō te rōrahi o te poraka, ngā mahi mō te tatau, ngā tauira, me ngā hapa noa.
1. Te Mārama ki ngā Poraka me ō rātou Āhuatanga
I mua i tā tātou urunga atu ki ngā tataunga, me mārama tātou he aha te poraka. He āhua āhuahanga toru-ahu te poraka, ā, e whai ake nei:
1. E 6 ngā taha he tapawhā katoa, he rite te rahi
2. 12 ngā rara he rite te roa
3. 8 ngā kokonga
4. He koki tika ngā koki katoa (90°)
Ko te mea nui ki te tatau i te rōrahi ko te roa o ngā tapa katoa o te poraka. Koia te take he tino māmā te tātai mō te rōrahi o te poraka.
2. He aha te Rōrahi?
Ki te kī māmā noa, ko te rōrahi he ine i te wāhi i roto i tētahi āhua toru-ahu. Mēnā he pouaka tā tātou, ko te rōrahi e tohu ana i te nui o te wai, te onepu, me ētahi atu mea rānei ka taea te uru ki roto i te pouaka.
I roto i ngā waeine, ka whakaatuhia te rōrahi i roto i:
– henimita pūtoru (cm³)
– mita pūtoru (m³)
– rita (L) mō te kaha wai (1 rita = 1000 cm³)
– miririta (mL) (1 mL = 1 cm³)
Nō reira, he hononga tata te rōrahi ki te ariā o te "ihirangi" me te "kaha".
3. Te Tātai mō te Rōrahi o te Poraka
Nā te mea he ōrite te roa o ngā taha o te poraka, ka tatauhia tōna rōrahi mā te whakarea i ngā taha kia toru ngā wā (roa × whānui × teitei). I roto i te poraka, ko te roa = whānui = teitei = s.
Te tātai mō te rōrahi o te poraka:
\[
V = s^3
\]
Ngā Mōhiohio:
– V = te rōrahi o te poraka
– s = te roa o te taha (te taha) o te poraka
– ko te tikanga o te s³ ko s × s × s
He tino whai hua tēnei tātai nā te mea kotahi anake te uara e hiahiatia ana kia mōhiotia e tātou, arā, ko te roa o te taha o te poraka.
4. Ngā Hipanga hei Tātai i te Rōrahi o te Poraka
Anei ngā mahi whānui hei tatau tika i te rōrahi o tētahi poraka:
Hipanga 1: Tāutuhia te roa o te taha o te poraka
I te nuinga o te wā ka hoatu te uara o te tapa i roto i te rapanga, hei tauira 5 cm, 0,2 m rānei.
Hipanga 2: Kia tino ōrite ngā waeine
Ki te hiahia koe ki te rahinga i roto i te cm³, me whakamahi ngā taha i roto i te cm. Ki te mea kei roto i te mita ngā taha, ka whakamahia te rahinga i roto i te m³.
Hipanga 3: Mono ki te tātai V = s³
Whakareatia te uara o s kia toru ngā wā.
Hipanga 4: Tuhia ngā hua me ō rātou waeine.
Kaua e wareware ki ngā waeine pūtoru (hei tauira, cm³, m³).
5. Tauira mō te Tātai i te Rōrahi o te Poraka
Hei whakamāmā ake i te mārama, me titiro tātou ki ētahi tauira.
Tauira 1
E 4 henemita te roa o te taha o tētahi poraka. Tātaihia tōna rōrahi.
Otinga:
\[
V = s^3 = 4^3 = 4 \times 4 \times 4 = 64
\]
Nō reira, ko te rōrahi o te poraka he 64 cm³.
Tauira 2
He 10 cm te roa o ngā tapa o tētahi poraka. He aha te rōrahi?
Otinga:
\[
V = 10^3 = 10 \whakanuia te 10 \whakanuia te 10 = 1000
\]
Te rōrahi o te poraka = 1000 cm³.
He mea whakamere, ko te 1000 cm³ he ōrite ki te 1 rita, nō reira ko te kaha o te poraka he tata ki te 1 rita.
Tauira 3 (waeine mita)
Ko te roa o te taha o te poraka he 0,5 m. Tātaihia te rōrahi o te poraka.
Otinga:
\[
V = 0,5^3 = 0,5 \whakanuia te 0,5 \whakanuia te 0,5 = 0,125
\]
Te rōrahi o te poraka = 0,125 m³.
6. Te Tatau i ngā Ripeka Mena e Mōhiotia ana te Rōrahi
I ētahi wā, kāore tātou e mōhio ki te roa o te tapa, engari ko tōna rōrahi. Mēnā ka pērā, ka taea e tātou te kimi i te roa o te tapa mā te whakamahi i te whakahuri o te poraka, arā, te pūtake poraka.
Mena:
\[
V = s^3
\]
Nā reira:
\[
s = \sqrt[3]{V}
\]
Tauira 4
Ko te rōrahi o tētahi poraka he 216 cm³. He aha te roa o tōna taha?
Otinga:
\[
s = \sqrt[3]{216} = 6
\]
Nā te mea ko te 6 × 6 × 6 = 216, ko te roa o te tapa he 6 cm.
Tauira 5
Ko te rōrahi o tētahi poraka he 125 m³. Tāutuhia ōna tapa.
Otinga:
\[
s = \sqrt[3]{125} = 5
\]
Nō reira, ko te roa o te taha o te poraka he 5 m.
7. Ngā Hapa Noa i te Tatau i te Rōrahi o te Poraka
Ahakoa he māmā te tauira, koinei ētahi hapa e kitea whānuitia ana:
1. Kua wareware ki ngā waeine pūtoru
Hei tauira, te tuhi i te "64 cm" i te wā e tika ana kia "64 cm³".
2. Te tatau hē i te mana o te toru
Tauira: te whakaaro 5³ = 15, engari ko te 5³ = 125.
3. Ngā waeine kore taurite
Hei tauira, he 20 cm te roa o te rara, engari e hiahia ana koe ki te hua i roto i te m³ me te kore e whakarerekē i ngā waeine.
4. Pōhēhē ki te horahanga o te mata o te poraka
Ko te tātai mō te horahanga mata ko 6s², he rerekē tēnei i te rōrahi (s³).
8. Te Whakamahinga o te Rōrahi Matapōkere i roto i te Oranga o Ia Rā
Ehara i te mea he whai hua te tatau i te rōrahi o te poraka i roto i ngā akoranga pāngarau anake, engari i te ao tūturu anō hoki, hei tauira:
– Tātaihia te kaha o tētahi pouaka rokiroki āhua poraka
– Whakatauhia te nui o ngā rauemi ka uru ki roto i te ipu
– Tātaihia te rōrahi o tētahi hua kua tākaihia
– Te whakamahere wāhi i roto i te hoahoa ā-roto, i te hanganga māmā rānei
Mā te mārama ki te ariā o te rōrahi, ka taea e tātou te whakatau tika ake i ngā whakaritenga mō te wāhi me te kaha.
Whakamutunga
He tino māmā te tatau i te rōrahi o tētahi poraka nā te mea he ōrite te roa o ngā tapa katoa. Ko te tātai i whakamahia ko:
\[
V = s^3
\]
Ko te mea nui mō te tatau tika ko te mōhio ki te roa o te tapa, te tatau tika i te poraka, me te tuhi i ngā waeine rōrahi ki te āhua poraka. Mena e mōhiotia ana te rōrahi, ka taea e tātou te kimi i te tapa mā te whakamahi i te pūtake poraka:
\[
s = \sqrt[3]{V}
\]
Mā te whakaharatau i ngā tauira pātai me te mārama ki ngā ariā, ka taea e koe te tatau i te rōrahi o tētahi mataono kia tere ake, kia tika ake hoki.
Ki te hiahia koe, ka taea e au te hanga i ngā pātai whakaharatau tekau me ngā whakautu hei whakapakari i tō māramatanga ki te rōrahi o te poraka.
