Pyramid yog daim duab peb sab, lub hauv paus ntawm uas yog polygon, thiab sab yog daim duab peb sab. Lub hexagonal pyramid yog nws daim ntawv tshwj xeeb. Tsis tas li ntawd, muaj lwm yam kev hloov pauv thaum nyob rau hauv lub hauv paus ntawm daim duab peb sab (xws li daim duab yog hu ua tetrahedron) muaj square, duab plaub, pentagon, thiab lwm yam nyob rau hauv kev txiav txim nce. Thaum tus naj npawb ntawm cov ntsiab lus dhau los ua tsis kawg, lub khob hliav qab tau txais.
Hexagonal pyramid
Feem ntau, qhov no yog ib qho ntawm cov ntsiab lus tshiab thiab nyuaj tshaj plaws hauv kev ua kom pom tseeb. Nws tau kawm qee qhov hauv qib 10-11 thiab tsuas yog qhov kev xaiv raug txiav txim siab thaum tus lej raug nyob ntawm lub hauv paus. Ib txoj haujlwm nyuaj tshaj plaws hauv kev xeem feem ntau cuam tshuam nrog cov kab lus no.
Thiab yog li ntawd, ntawm lub hauv paus ntawm ib lub hexagonal pyramid li niaj zaus hexagon. Nws txhais li cas? Ntawm lub hauv paus ntawm daim duab, txhua sab yog sib npaug. Cov sab seem muaj cov duab peb sab isosceles. Lawv vertices kov ntawm ib qho chaw. Daim duab nopom hauv daim duab hauv qab no.
Yuav ua li cas thiaj nrhiav tau tag nrho thaj chaw saum npoo thiab ntim ntawm hexagonal pyramid?
Tsis zoo li kev lej qhia hauv tsev kawm qib siab, tsev kawm ntawv kev tshawb fawb qhia kom hla dhau thiab ua kom yooj yim rau qee lub tswv yim nyuaj. Piv txwv li, yog tias nws tsis paub yuav ua li cas nrhiav thaj tsam ntawm daim duab, ces koj yuav tsum faib nws mus rau hauv qhov chaw thiab nrhiav cov lus teb siv cov qauv uas twb paub lawm rau thaj chaw ntawm cov duab faib. Lub hauv paus ntsiab lus no yuav tsum tau ua raws li hauv rooj plaub uas tau nthuav tawm.
Yog, txhawm rau nrhiav thaj chaw ntawm tag nrho hexagonal pyramid, koj yuav tsum nrhiav thaj tsam ntawm lub hauv paus, tom qab ntawd thaj tsam ntawm ib sab thiab muab faib ua 6.
Cov qauv hauv qab no siv:
S (full)=6S (sab) + S (base), (1);
S (bases)=3√3 / 2a2, (2);
6S (sab)=6 × 1 / 2ab=3ab, (3);
S (full)=3ab + (3√3 / 2a2)=3(2a2b + √3) / 2a2, (4).
S yog thaj chaw, cm2;
a - puag ntev, cm;
b - apothem (qhov siab ntawm sab ntsej muag), saib
txhawm rau txhawm rau nrhiav thaj tsam ntawm tag nrho saum npoo lossis ib qho ntawm nws cov khoom, tsuas yog sab ntawm lub hauv paus ntawm lub hauv paus ntawm lub hexagonal pyramid thiab apothem. Yog tias qhov no tau muab rau hauv cov xwm txheej hauv qhov teeb meem, ces qhov kev daws yuav tsis nyuaj.
Yam yooj yim dua nrog ntim, tab sis txhawm rau nrhiav nws, koj xav tau qhov siab (h) ntawm hexagonal pyramid nws tus kheej. Thiab, tau kawg, sab ntawm lub hauv paus, ua tsaug uas koj yuav tsum nrhiav nws thaj chaw.
Formulazoo li no:
V=1/3 × S (bases) × h, (5).
V nyob qhov twg, sm3;
h - daim duab qhov siab, saib
Teeb meem variant uas tuaj yeem ntes tau ntawm kev xeem
Zoo. Muab ib tug li niaj zaus hexagonal pyramid. Qhov ntev ntawm lub hauv paus yog 3 cm Qhov siab yog 5 cm Nrhiav qhov ntim ntawm daim duab no.
Solution: V=1/3 × (3√3/2 × 32) × 5=5/3 × √3/6=5√3/18.
Teb: qhov ntim ntawm ib lub hexagonal pyramid li niaj zaus yog 5√3/18 cm.
