Yuav Ua Li Cas Xam Qhov Ntim ntawm Lub Cube
Lub voos xwmfab yog ib qho ntawm cov duab geometric uas paub zoo tshaj plaws hauv kev lej. Nws yog symmetrical, nrog rau txhua sab sib npaug, thiab peb ntsib nws ntau zaus hauv lub neej txhua hnub - los ntawm cov dice mus rau cov thawv khoom plig zoo li voos xwmfab mus rau ntau yam qauv cia khoom. Ib qho ntawm cov hauv paus uas yuav tsum nkag siab thaum kawm txog voos xwmfab yog yuav ua li cas xam lawv qhov ntim. Qhov ntim ntawm lub voos xwmfab qhia tau tias lub voos xwmfab tuaj yeem tuav tau qhov chaw ntau npaum li cas. Tsab xov xwm no yuav tham txog kev txhais ntawm qhov ntim, cov mis rau qhov ntim ntawm lub voos xwmfab, cov kauj ruam rau kev xam nws, piv txwv, thiab cov yuam kev feem ntau.
1. Nkag Siab Txog Cov Cubes Thiab Lawv Cov Khoom
Ua ntej peb yuav pib suav, peb yuav tsum nkag siab tias lub voos xwmfab yog dab tsi. Lub voos xwmfab yog ib daim duab peb sab uas muaj:
1. 6 sab uas yog plaub fab thiab loj ib yam
2. 12 tav ntawm qhov ntev sib npaug
3. 8 lub ces kaum
4. Txhua lub kaum sab xis yog lub kaum sab xis (90°)
Tus yuam sij rau kev xam qhov ntim yog tias txhua ntug ntawm lub voos xwmfab yuav tsum ntev tib yam. Qhov no yog vim li cas cov mis rau qhov ntim ntawm lub voos xwmfab thiaj yooj yim heev.
2. Ntim yog dab tsi?
Hais yooj yim xwb, qhov ntim yog qhov ntsuas qhov chaw hauv ib daim duab peb sab. Yog tias peb muaj ib lub thawv, qhov ntim qhia tias muaj pes tsawg dej, xuab zeb, lossis lwm yam khoom tuaj yeem tso rau hauv lub thawv.
Hauv cov units, qhov ntim feem ntau yog qhia hauv:
- cubic centimeter (cm³)
- cubic meters (m³)
– litres (L) rau cov kua muaj peev xwm (1 liter = 1000 cm³)
– milliliter (mL) (1 mL = 1 cm³)
Yog li, qhov ntim muaj feem cuam tshuam nrog lub tswv yim ntawm "cov ntsiab lus" lossis "muaj peev xwm".
3. Cov Qauv rau Qhov Ntim ntawm Lub Cube
Vim tias ib lub voos xwmfab muaj cov sab uas ntev sib npaug zos, nws qhov ntim yog xam los ntawm kev muab cov sab sib npaug zos peb zaug (ntev × dav × siab). Hauv ib lub voos xwmfab, ntev = dav = siab = s.
Cov mis rau qhov ntim ntawm lub voos xwmfab:
\[
V = s^3
\]
Cov Ntaub Ntawv:
- V = volume ntawm lub voos xwmfab
- s = ntev ntawm ntug (sab) ntawm lub voos xwmfab
– s³ txhais tau tias s × s × s
Cov mis no siv tau zoo heev vim peb tsuas xav paub ib qho nqi xwb, uas yog qhov ntev ntawm ntug ntawm lub voos xwmfab.
4. Cov Kauj Ruam Los Xam Qhov Ntim ntawm Lub Cube
Nov yog cov kauj ruam dav dav los xam qhov ntim ntawm lub voos xwmfab kom raug:
Kauj Ruam 1: Txheeb xyuas qhov ntev ntawm ntug ntawm lub voos xwmfab (s)
Feem ntau tus nqi ntawm ntug yog muab rau hauv qhov teeb meem, piv txwv li 5 cm lossis 0,2 m.
Kauj Ruam 2: Xyuas kom tseeb tias cov units sib xws
Yog koj xav tau qhov ntim hauv cm³, ces cov sab yuav tsum yog cm. Yog tias cov sab yog meters, qhov ntim yuav yog m³.
Kauj Ruam 3: Txuas rau hauv tus qauv V = s³
Muab tus nqi ntawm s sib npaug peb zaug.
Kauj Ruam 4: Sau cov txiaj ntsig nrog rau lawv cov units.
Tsis txhob hnov qab cov cubic units (piv txwv li cm³, m³).
5. Piv txwv ntawm kev xam qhov ntim ntawm lub voos xwmfab
Yuav kom yooj yim to taub, cia peb saib qee qhov piv txwv.
Piv txwv 1
Muab hais tias ib lub voos xwmfab muaj ib sab ntev li 4 cm. Xam nws qhov ntim.
Kev daws teeb meem:
\[
V = s^3 = 4^3 = 4 \times 4 \times 4 = 64
\]
Yog li, qhov ntim ntawm lub voos xwmfab yog 64 cm³.
Piv txwv 2
Ib lub voos xwmfab muaj cov npoo ntsuas 10 cm. Nws qhov ntim yog dab tsi?
Kev daws teeb meem:
\[
V = 10^3 = 10 \times 10 \times 10 = 1000
\]
Qhov ntim ntawm ib lub voos xwmfab = 1000 cm³.
Qhov nthuav yog, 1000 cm³ yog sib npaug rau 1 liter, yog li lub voos xwmfab muaj peev xwm kwv yees li 1 liter.
Piv txwv 3 (chav ntsuas)
Qhov ntev ntawm ntug ntawm lub voos xwmfab yog 0,5 m. Xam qhov ntim ntawm lub voos xwmfab.
Kev daws teeb meem:
\[
V = 0,5^3 = 0,5 \times 0,5 \times 0,5 = 0,125
\]
Qhov ntim ntawm lub voos xwmfab = 0,125 m³.
6. Xam Qhov Ntev Yog Paub Qhov Ntim
Qee zaum peb tsis paub qhov ntev ntawm ntug, tab sis peb tsis paub nws qhov ntim. Yog li ntawd, peb tuaj yeem nrhiav qhov ntev ntawm ntug los ntawm kev siv qhov tig rov qab ntawm lub voos xwmfab, uas yog lub hauv paus voos xwmfab.
Yog tias:
\[
V = s^3
\]
Yog li ntawd:
\[
s = \sqrt[3]{V}
\]
Piv txwv 4
Lub ntim ntawm ib lub voos xwmfab yog 216 cm³. Nws ntug ntev npaum li cas?
Kev daws teeb meem:
\[
s = \sqrt[3]{216} = 6
\]
Txij li thaum 6 × 6 × 6 = 216, qhov ntev ntawm ntug yog 6 cm.
Piv txwv 5
Lub ntim ntawm ib lub voos xwmfab yog 125 m³. Txheeb xyuas nws cov npoo.
Kev daws teeb meem:
\[
s = \sqrt[3]{125} = 5
\]
Yog li ntawd, qhov ntev ntawm ntug ntawm lub voos xwmfab yog 5 m.
7. Cov Yuam Kev Feem Ntau Thaum Xam Qhov Ntim ntawm Lub Cube
Txawm hais tias cov mis no yooj yim los xij, cov no yog qee qhov yuam kev uas feem ntau tshwm sim:
1. Tsis nco qab cov cubic units
Piv txwv li, sau "64 cm" thaum nws yuav tsum yog "64 cm³".
2. Xam lub zog ntawm peb yam tsis raug
Piv txwv li: xav tias 5³ = 15, thaum qhov tseeb 5³ = 125.
3. Cov chav tsis sib xws
Piv txwv li, tus tav yog 20 cm tab sis koj xav tau qhov tshwm sim hauv m³ yam tsis hloov pauv cov chav.
4. Tsis meej pem nrog thaj tsam ntawm lub voos xwmfab
Cov mis rau thaj tsam ntawm qhov chaw yog 6s², uas txawv ntawm qhov ntim (s³).
8. Kev Siv Lub Cube Volume Hauv Lub Neej Txhua Hnub
Kev suav qhov ntim ntawm lub voos xwmfab tsis yog tsuas yog muaj txiaj ntsig zoo rau kev kawm lej xwb, tab sis kuj tseem muaj txiaj ntsig zoo rau lub neej tiag tiag, piv txwv li:
- Xam qhov muaj peev xwm ntawm lub thawv cia khoom zoo li lub voos xwmfab
- Txheeb xyuas seb cov khoom siv yuav haum rau hauv lub thawv ntau npaum li cas
- Xam qhov ntim ntawm cov khoom ntim tshwj xeeb
- Kev npaj chaw hauv kev tsim sab hauv lossis kev tsim kho yooj yim
Los ntawm kev nkag siab txog lub tswv yim ntawm qhov ntim, peb tuaj yeem kwv yees qhov chaw thiab qhov muaj peev xwm xav tau kom raug dua.
Xaus
Xam qhov ntim ntawm lub voos xwmfab yooj yim heev vim tias txhua ntug ntev ib yam. Cov mis siv yog:
\[
V = s^3
\]
Tus yuam sij rau kev xam kom raug yog paub qhov ntev ntawm ntug, xam lub voos xwmfab kom raug, thiab sau cov chav ntim hauv daim ntawv voos xwmfab. Yog tias paub qhov ntim, peb tuaj yeem nrhiav ntug siv cov hauv paus voos xwmfab:
\[
s = \sqrt[3]{V}
\]
Los ntawm kev xyaum cov lus nug piv txwv thiab nkag siab cov ntsiab lus, koj yuav muaj peev xwm xam qhov ntim ntawm lub voos xwmfab sai dua thiab raug dua.
Yog tias koj xav tau, kuv kuj tuaj yeem ua 10 lo lus nug xyaum nrog cov lus teb los txhawb koj txoj kev nkag siab txog qhov ntim ntawm lub voos xwmfab.
