Lub voos xwmfab yog cov duab peb sab uas muaj qhov ntev tib yam, dav thiab qhov siab. Ib lub voos xwmfab muaj rau rau sab plaub fab, txhua qhov uas yog qhov ntev thiab sib ntsib ntawm cov ces kaum raug. Nrhiav qhov ntim ntawm lub voos xwmfab yog qhov yooj yim heev, txhua yam koj xav tau yog los xam ntev × dav × qhov siab Lub voos xwmfab. Txij li txhua lub npoo ntawm lub voos xwmfab yog qhov ntev tib yam, lwm txoj hauv kev los laij qhov ntim yog s 3, qhov twg s yog qhov ntev ntawm ib sab ntawm lub voos xwmfab. Nyeem Kauj Ruam 1 hauv qab no kom nkag siab cov ncauj lus ntxaws ntawm cov txheej txheem no.
Kauj ruam
Txoj Kev 1 ntawm 3: Tsa Lub Cube Peb Qhov Ntug
Kauj Ruam 1. Nrhiav qhov ntev ntawm sab ntawm lub voos xwmfab
Feem ntau, yog qhov teeb meem nug txog qhov ntim ntawm lub voos xwmfab, koj yuav muab qhov ntev ntawm sab. Yog tias muaj, koj muaj txhua yam koj xav tau los nrhiav qhov ntim ntawm lub voos xwmfab. Yog tias koj tsis ua qhov teeb meem, tab sis hloov qhov suav thawj lub voos xwmfab, ntsuas cov ntug nrog tus pas ntsuas lossis ntsuas ntsuas.
Txhawm rau nkag siab cov txheej txheem ntawm kev nrhiav lub ntim ntawm lub voos xwmfab zoo dua, cia ua raws qhov piv txwv teeb meem thaum peb mus dhau cov theem hauv ntu no. Hais tias lub voos xwmfab muaj ob sab ntev 2 cm. Cov ntaub ntawv no yuav siv los nrhiav qhov ntim ntawm lub voos xwmfab hauv cov kauj ruam tom ntej
Kauj Ruam 2. Txiav lub voos xwmfab sab ntev
Yog tias koj paub qhov ntev ntawm ib sab ntawm lub voos xwmfab, tsa nws kom muaj zog peb. Hauv lwm lo lus, suav nrog tus lej nws tus kheej ob zaug. Yog s yog qhov ntev ntawm ntug, muab sib npaug s × s × s (lossis yooj yim, s 3). Qhov tshwm sim yog qhov ntim ntawm koj lub voos xwmfab!
- Hauv qhov tseeb, cov txheej txheem no zoo ib yam li nrhiav thaj tsam ntawm lub hauv paus thiab muab nws sib npaug los ntawm qhov siab (hauv lwm lo lus, qhov ntev × dav × qhov siab) vim tias thaj tsam ntawm lub hauv paus tau txais los ntawm kev sib npaug qhov ntev thiab dav. Txij li lub voos xwmfab yog cov duab uas muaj qhov zoo ib yam ntev, dav, thiab qhov siab, cov txheej txheem no tuaj yeem luv dua los ntawm kev sib npaug los ntawm peb.
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Cia peb txuas ntxiv peb qhov teeb meem piv txwv. Txij li sab ntawm lub voos xwmfab yog 2 cm, nws lub ntim tuaj yeem suav tau los ntawm kev sib npaug 2 x 2 x 2 (lossis 23) =
Kauj ruam 8..
Kauj Ruam 3. Muab cov khoom ntim hauv cubic
Txij li qhov ntim yog ntsuas ntawm qhov chaw peb-seem, koj cov lus teb yuav tsum muaj chav ntsuas. Feem ntau, koj cov lus teb tseem yuav raug liam yog tias chav tsev tsis yog cubic, txawm tias tus lej raug. Yog li, tsis txhob hnov qab muab chav nyob kom raug.
- Hauv qhov teeb meem piv txwv, txij li thawj chav tsev yog centimeters (cm), cov lus teb kawg yuav tsum muaj chav ntawm "cubic centimeter" (lossis cm.).3). Yog li, peb cov lus teb yog 8 cmj3.
- Yog tias qhov ntev ntawm ntug ntawm lub voos xwmfab siv chav sib txawv, cov chav ntim khoom yuav tsum tau hloov kho. Piv txwv li, yog tias sab ntawm lub voos xwmfab yog 2 "metres" hloov ntawm centimeters, chav kawg ntawm ntim yog kub meter (m3).
Txoj Kev 2 ntawm 3: Nrhiav Ntim Los Ntawm Qhov Chaw
Kauj Ruam 1. Nrhiav thaj tsam ntawm lub voos xwmfab
Txawm yog txoj kev yooj yim tshaj plaws txhawm rau nrhiav qhov ntim ntawm lub voos xwmfab yog siv ib qho ntawm cov npoo, tseem muaj lwm txoj kev mus nrhiav nws. Sab ntev ntawm lub voos xwmfab lossis thaj tsam ntawm lub xwmfab ntawm ib ntawm nws lub ntsej muag tuaj yeem muab tau los ntawm qee qhov lwm yam ntawm lub voos xwmfab, uas txhais tau tias yog koj pib nrog ib qho ntawm cov ntaub ntawv no, ntim ntawm lub voos xwmfab tuaj yeem ua tau yuav pom los ntawm txoj siav. Piv txwv li, yog tias koj paub thaj tsam ntawm lub voos xwmfab, nws ntim tau pom nrog faib qhov saum npoo los ntawm 6, tom qab ntawd hauv paus kom pom sab ntev ntawm lub voos xwmfab.
Los ntawm no, ntim tuaj yeem tshawb hauv txoj hauv kev ib txwm muaj hauv Txoj Kev 1. Hauv ntu no, peb yuav mus dhau cov txheej txheem ib qib zuj zus.
- Qhov saum npoo ntawm lub voos xwmfab yog pom los ntawm cov mis 6 nqi s 2, qhov twg s yog qhov ntev ntawm ib qho ntawm cov npoo ntawm lub voos xwmfab. Cov mis no yog qhov tseem ceeb tib yam li nrhiav thaj tsam thaj tsam ntawm 2-dimensional shape ntawm rau ntawm ob sab ntawm lub voos xwmfab, tom qab ntawd ntxiv lawv tag nrho ua ke. Peb yuav siv cov mis no los nrhiav qhov ntim ntawm ib lub voos xwmfab los ntawm nws thaj chaw.
- Piv txwv li, hais tias peb muaj lub voos xwmfab uas nws thaj tsam yog 50 cm ib2, tab sis qhov ntev ntawm tus tav tsis paub. Hauv ob peb kauj ruam tom ntej, peb yuav siv cov ntaub ntawv no los nrhiav qhov ntim ntawm lub voos xwmfab.
Kauj Ruam 2. Faib thaj tsam ntawm lub voos xwmfab nrog 6
Txij li thaum lub voos xwmfab muaj 6 sab sib npaug, thaj tsam ntawm ib sab tuaj yeem tau txais los ntawm thaj tsam ntawm ib lub voos xwmfab nrog 6. Lub cheeb tsam ntawm ib sab yog sib npaug ntawm cov khoom ntawm ob ntug ntawm lub voos xwmfab (ntev × dav, dav × qhov siab, lossis qhov siab × ntev).
Hauv qhov piv txwv no, faib 50/6 = 8, 33 cmj2. Tsis txhob hnov qab tias daim duab ob-seem muaj chav nyob xwmfab (cm ntev2, m ua2, thiab lwm yam).
Kauj Ruam 3. Hauv paus qhov suav qhov tshwm sim
Txij li thaj tsam ntawm ib sab ntawm lub voos xwmfab yog s 2 (s × s), noj cov hauv paus no yuav ua rau koj qhov ntev ntawm ib sab ntawm lub voos xwmfab. Thaum koj paub sab ntev, koj tuaj yeem pom qhov ntim ntawm lub voos xwmfab siv cov qauv ib txwm muaj.
Hauv qhov teeb meem piv txwv, 8, 33 ntau dua lossis tsawg dua 2, 89 cmj.
Kauj Ruam 4. Tsa tus ntug ntawm lub voos xwmfab peb zaug kom tau txais lub ntim ntawm lub voos xwmfab
Tam sim no koj muaj qhov ntev ntawm ib sab ntawm lub voos xwmfab, tsuas yog lub voos xwmfab uas muaj nuj nqis (suav nrog tus lej nws tus kheej ob zaug) txhawm rau nrhiav qhov ntim ntawm lub voos xwmfab raws li cov kauj ruam hauv Txoj Kev 1. Ua tsaug, koj tau pom qhov ntim ntawm lub voos xwmfab los ntawm nws thaj chaw.
Hauv qhov teeb meem piv txwv, 2, 89 × 2, 89 × 2, 89 = 24,14 cm ib3. Tsis txhob hnov qab ntxiv cubic units rau koj cov lus teb.
Txoj Kev 3 ntawm 3: Nrhiav Ntim Ntawm Kab Kab Ntsig
Kauj Ruam 1. Faib kab pheeb ces kaum ntawm ib sab ntawm lub voos xwmfab los ntawm 2 kom pom cov ntug
Kab pheeb ces kaum ntawm ib lub xwmfab yog 2 × qhov ntev ntawm sab. Yog li, yog tias cov ntaub ntawv muab tsuas yog kab pheeb ces kaum ntawm ib sab ntawm lub voos xwmfab, koj tuaj yeem pom ntug los ntawm kev faib cov kab pheeb ces kaum ntawm 2. Los ntawm no, koj tuaj yeem tshawb nrhiav qhov ntim nrog cov kauj ruam hauv Txoj Kev 1.
- Piv txwv, hais tias ib sab ntawm lub voos xwmfab muaj kab pheeb ces kaum ntawm 7 cmj. Peb yuav pom sab ntev ntawm lub voos xwmfab los ntawm kev suav 7/√2 = 4.96 cm. Tam sim no koj paub qhov ntev npaum li cas, lub ntim tuaj yeem suav los ntawm kev suav 4.963 = 122, 36 cm ib3.
- Nws yuav tsum tau sau tseg, feem ntau, tias d 2 = 2 tus 2 uas yog, d yog qhov ntev ntawm kab pheeb ces kaum ntawm ib sab ntawm lub voos xwmfab, thiab s yog qhov ntev ntawm ib sab ntawm lub voos xwmfab. Qhov no yog ua raws Pythagorean Theory, uas hais tias lub xwmfab ntawm qhov hypotenuse ntawm daim duab peb sab xis yog sib npaug ntawm cov xwm txheej ntawm ob sab. Yog li, txij li kab pheeb ces kaum ntawm ib sab ntawm lub voos xwmfab thiab nws ob sab yog daim duab peb sab xis, d 2 = tus 2 + tus s 2 = 2 tus 2.
Kauj Ruam 2. Muab kab pheeb ces kaum sib txuas ntawm ob lub kaum sab xis sib npaug ntawm lub voos xwmfab, tom qab ntawd faib los ntawm 3 thiab cov hauv paus plaub fab kom tau txais qhov ntev ntawm sab
Yog tias cov ntaub ntawv muab tsuas yog peb kab pheeb ces kaum ntawm lub voos xwmfab nthuav tawm los ntawm ib ces kaum ntawm lub voos xwmfab mus rau kaum lub kaum sab xis nws, qhov ntim ntawm lub voos xwmfab tseem tuaj yeem pom. Peb-kab pheeb ces kaum ntawm D dhau los ua qhov hypotenuse ntawm daim duab peb sab tsim nrog lub voos plaub ntug, thiab kab pheeb ces kaum ntawm lub xwmfab ntawm ib sab ntawm lub voos xwmfab "d". Hauv lwm lo lus, D. 2 = 3s 2, piv txwv li D = kab pheeb ces kaum ntawm 3-seem duab txuas sib thooj ntawm lub voos xwmfab.
- Qhov no yog vim Pythagorean Theory. D, d, thiab s tsim lub kaum sab xis nrog D ua qhov hypotenuse, yog li peb tuaj yeem hais tias D 2 = d 2 + tus s 2. Yog li saum toj no peb suav d 2 = 2 tus 2, nws paub tseeb tias D. 2 = 2 tus 2 + tus s 2 = 3s 2.
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Piv txwv li, cia peb hais tias peb paub tias qhov ntev ntawm kab pheeb ces kaum sib txuas ib qho ntawm cov ces kaum ntawm lub hauv paus ntawm lub voos xwmfab mus rau kaum lub kaum sab xis nws sab saum toj yog 10 m. Txhawm rau nrhiav qhov ntim, sau 10 rau txhua "D" hauv kab zauv:
- D 2 = 3s 2.
- 102 = 3s 2.
- 100 = 3s 2
- 33, 33 = np 2
- 5,77m ua = tus Txij ntawm no, peb tsuas yog xav nrhiav qhov ntim ntawm lub voos xwmfab siv sab ntev.
- 5, 773 = 192, 45m ib3
