Regular hexagonal pyramid. Cov qauv rau qhov ntim thiab qhov chaw. Kev daws teeb meem geometric

2024 Tus sau: Angel Austin | [email protected]. Kawg hloov kho: 2024-01-02 17:48

Stereometry, ua ib ceg ntawm geometry hauv qhov chaw, kawm txog cov khoom ntawm prisms, cylinders, cones, pob, pyramids thiab lwm yam duab peb sab. Kab lus no tau mob siab rau kev tshuaj xyuas cov yam ntxwv thiab cov khoom ntawm hexagonal li niaj zaus pyramid.

Yuav ua li cas pyramid yuav kawm

Ib lub hexagonal pyramid tsis tu ncua yog ib daim duab hauv qhov chaw, uas yog txwv los ntawm ib qho sib npaug thiab sib npaug hexagon, thiab rau qhov zoo tib yam isosceles daim duab peb sab. Cov duab peb sab no tuaj yeem sib npaug hauv qee qhov xwm txheej. Lub pyramid no tau qhia hauv qab no.

Tus tib daim duab yog qhia ntawm no, tsuas yog nyob rau hauv ib rooj plaub nws tig nrog nws sab sab ntawm tus nyeem ntawv, thiab nyob rau hauv lwm yam - nrog nws sab ntug.

Ib lub hexagonal pyramid ib txwm muaj 7 lub ntsej muag, uas tau hais los saum no. Nws kuj muaj 7 vertices thiab 12 ntug. Tsis zoo li prisms, tag nrho cov pyramids muaj ib qho tshwj xeeb vertex, uas yog tsim los ntawm kev sib tshuam ntawm sab.daim duab peb sab. Rau lub pyramid tsis tu ncua, nws ua lub luag haujlwm tseem ceeb, txij li lub perpendicular qis los ntawm nws mus rau lub hauv paus ntawm daim duab yog qhov siab. Tsis tas li ntawd, qhov siab yuav txhais los ntawm tsab ntawv h.

Lub pyramid uas pom tau raug hu raug rau ob qho laj thawj:

• ntawm nws lub hauv paus yog hexagon nrog qhov sib npaug ntawm sab ntev thiab cov kaum sib npaug ntawm 120o;
• Qhov siab ntawm lub pyramid h cuam tshuam lub hexagon raws nraim ntawm nws qhov chaw (qhov taw qhia ntawm kev sib tshuam nyob ntawm tib qhov deb ntawm txhua sab thiab los ntawm tag nrho cov vertices ntawm lub hexagon).

Ntog cheeb tsam

Cov khoom ntawm ib txwm hexagonal pyramid yuav raug txiav txim siab los ntawm lub ntsiab lus ntawm nws cheeb tsam. Ua li no, nws yog thawj qhov tseem ceeb rau nthuav tawm daim duab ntawm lub dav hlau. Ib tug schematic sawv cev ntawm nws yog qhia hauv qab no.

Nws tuaj yeem pom tau tias thaj tsam ntawm qhov cheb, thiab yog li tag nrho saum npoo ntawm daim duab nyob rau hauv kev txiav txim siab, yog sib npaug rau qhov sib npaug ntawm thaj tsam ntawm 6 daim duab peb sab thiab ib hexagon.

Txhim kho thaj tsam ntawm hexagon S_{6, siv cov mis universal rau ib txwm n-gon:}

S=n/4a2ctg(pi/n)=>

S₆=3√3/2a^2.

Qhov twg yog qhov ntev ntawm sab ntawm hexagon.

thaj tsam ntawm daim duab peb sab S₃ ntawm sab sab tuaj yeem pom yog tias koj paub tus nqi ntawm nws qhov siab h_b:

S₃=1/2h_ba.

Vim tag nrho raudaim duab peb sab sib npaug rau ib leeg, ces peb tau txais kev qhia ua haujlwm rau kev txiav txim siab thaj tsam ntawm hexagonal pyramid nrog lub hauv paus raug:

S=S₆+ 6S₃=3√3/2a^{2 + 61/2h}b_{a=3a(√3/2a + h}b_).

Pyramid ntim

Ib yam li thaj chaw, qhov ntim ntawm hexagonal li niaj zaus pyramid yog nws cov khoom tseem ceeb. Qhov ntim no yog xam los ntawm cov qauv dav dav rau tag nrho cov pyramids thiab cones. Wb sau cia:

V=1/3S_oh.

Ntawm no, lub cim S_o yog thaj tsam ntawm lub hauv paus hexagonal, i.e. S_o=S _6.

Hloov cov lus qhia saum toj no rau S_{6 rau hauv cov qauv rau V, peb tuaj txog ntawm qhov sib npaug kawg rau kev txiav txim siab qhov ntim ntawm ib qho hexagonal pyramid:}

V=√3/2a2h.

Ib qho piv txwv ntawm qhov teeb meem geometric

Nyob rau hauv ib lub hexagonal pyramid li niaj zaus, sab ntug yog ob npaug ntawm qhov ntev ntawm lub hauv paus sab. Paub tias tom kawg yog 7 cm, nws yog ib qho tsim nyog los xam qhov chaw saum npoo thiab ntim ntawm daim duab no.

Raws li koj xav, qhov kev daws teeb meem no suav nrog kev siv cov lus hais saum toj no rau S thiab V. Txawm li cas los xij, nws yuav siv tsis tau tam sim ntawd, vim peb tsis paub lub npe thiab tus qhov siab ntawm ib txwm hexagonal pyramid. Cia peb suav lawv.

The apothem h_b tuaj yeem txiav txim siab los ntawm kev txiav txim siab ntawm txoj cai daim duab peb sab ua rau sab b, a/2 thiab h_{b. Ntawm no b yog qhov ntev ntawm sab ntug. Siv cov xwm txheej ntawm qhov teeb meem, peb tau txais:}

h_b=√(b²-a²/4)=√(14 ²-7^{2/4)=13, 555 cm.}

Qhov siab h ntawm lub pyramid tuaj yeem txiav txim siab tib yam nkaus li kev hais lus, tab sis tam sim no peb yuav tsum xav txog ib daim duab peb sab nrog sab h, b thiab a, nyob rau hauv lub pyramid. Qhov siab yuav yog:

h=√(b²- a²)=√(14²- 7 ^{2)=12, 124 cm.}

Nws tuaj yeem pom tau tias qhov ntsuas qhov siab tus nqi tsawg dua li qhov apothem, uas yog qhov tseeb rau txhua lub pyramid.

Tam sim no koj tuaj yeem siv cov lus qhia rau ntim thiab cheeb tsam:

S=3a(√3/2a + h_b)=37(√3/27 + 13, 555)=411, 96cm^2;

V=√3/2a²h=√3/27²12, 124=514, 48cm^3.

Yog li, txhawm rau txiav txim siab tsis meej txog txhua yam ntawm cov kab ke hexagonal li niaj zaus, koj yuav tsum paub ob qho ntawm nws cov kab tsis sib xws.