Yuav ua li cas kos lub pentagonal prism? Volume thiab deg cheeb tsam ntawm ib daim duab

2024 Tus sau: Angel Austin | [email protected]. Kawg hloov kho: 2023-12-17 05:28

Lub pentagonal prism hauv kev daws teeb meem hauv geometry yog qhov tsawg dua li cov prisms xws li daim duab peb sab, plaub fab lossis hexagonal. Txawm li cas los xij, nws yog qhov tseem ceeb los tshuaj xyuas cov khoom tseem ceeb ntawm cov duab no, nrog rau kawm paub kos nws.

Pentagonal prism yog dab tsi?

Qhov no yog daim duab peb sab, lub hauv paus uas yog pentagons, thiab sab yog parallelograms. Yog hais tias txhua yam ntawm cov parallelograms yog perpendicular mus rau lub hauv paus thaum uas tig mus, ces xws li ib tug prism yog hu ua rectangular. Sab nraub qaum ntawm ib lub duab plaub pentagonal prism yog tsim los ntawm tsib lub duab plaub. Ntxiv mus, sab uas nyob ib sab ntawm lub hauv paus ntawm txhua tus ntawm lawv yog sib npaug rau qhov sib txuas ntev ntawm sab ntawm pentagon.

Yog hais tias lub pentagon tsis tu ncua, uas yog, tag nrho nws ob sab thiab lub kaum sab xis yog sib npaug rau ib leeg, ces xws li lub prism yog hu ua tsis tu ncua. Ntxiv rau hauv tsab xov xwm peb yuav xav txog cov khoom ntawm daim duab no.

Prism ntsiab

Rau nws, rau txhua qhov prism,Cov hauv qab no yog cov yam ntxwv:

• ntsej muag lossis ob sab yog qhov ntawm cov dav hlau uas khi ib daim duab hauv qhov chaw;
• top - cov ntsiab lus ntawm kev sib tshuam ntawm peb sab;
• ribs - ntu ntawm kev sib tshuam ntawm ob sab ntawm daim duab.

Tus lej ntawm txhua lub npe muaj feem cuam tshuam rau ib leeg los ntawm kev sib npaug hauv qab no:

Number of edges=number of vertices + number of faces - 2

Qhov kev qhia no yog hu ua Euler formula rau polyhedron.

Nyob rau hauv lub pentagonal prism, tus naj npawb ntawm sab yog xya (ob lub hauv paus + tsib daim duab plaub). Tus naj npawb ntawm cov peaks yog 10 (tsib rau txhua lub hauv paus). Tus naj npawb ntawm cov npoo hauv qhov no yuav yog:

ntau tus tav=10 + 7 - 2=15

Kaum npoo yog rau lub hauv paus ntawm prism, thiab tsib npoo yog tsim los ntawm cov duab plaub.

Yuav ua li cas kos lub pentagonal prism?

Cov lus teb rau lo lus nug no nyob ntawm txoj haujlwm tshwj xeeb. Yog hais tias nws yog tsim nyog los kos ib arbitrary prism, ces txhua pentagon yuav tsum tau kos. Tom qab ntawd, kos tsib ntu ntawm qhov sib npaug ntawm qhov sib npaug ntawm txhua qhov vertex ntawm pentagon. Tom qab ntawd, txuas lub sab sauv kawg ntawm ntu. Qhov tshwm sim yog lub pentagonal arbitrary prism.

Yog tias nws tsim nyog los kos lub prism tsis tu ncua, ces tag nrho cov kev nyuaj ntawm txoj hauj lwm nqis los kom tau txais lub pentagon tsis tu ncua. Muaj ntau ntau txoj hauv kev los kos tus polygon no. Ntawm no peb yuav txiav txim siab tsuas yog ob txoj hauv kev.

Thawj txoj hauv kev yog kos ib lub voj voog nrog lub koob. Ces ib tug arbitrary txoj kab uas hla yog koslub voj voog thiab tsib lub kaum sab xis suav los ntawm nws siv lub protractor ntawm 72^o(572^o=360^{o). Thaum suav txhua lub kaum sab xis, ib qho notch yog ua rau ntawm lub voj voog. Txhawm rau tsim ib daim duab plaub, nws tseem yuav txuas cov cim kos nrog ntu ncaj.}

Txoj kev thib ob tsuas yog siv lub tshuab raj thiab tus kav xwb. Nws yog me ntsis nyuaj nyob rau hauv kev sib piv nrog rau yav dhau los. Hauv qab no yog ib daim vis dis aus uas piav qhia meej txhua kauj ruam ntawm qhov tsim no.

Nco ntsoov tias nws yooj yim los kos lub pentagon yog tias koj txuas qhov kawg ntawm lub hnub qub. Yog tias nws tsis tsim nyog los kos lub pentagon raws nraim li niaj zaus, koj tuaj yeem siv lub hnub qub kos duab tes.

Thaum lub pentagon tau kos, kos tsib qhov sib npaug sib npaug ntawm txhua qhov ntawm nws cov vertices thiab txuas lawv cov vertices. Qhov tshwm sim yog lub pentagonal prism.

Zoo cheeb tsam

Tam sim no xav txog yuav ua li cas nrhiav thaj tsam ntawm pentagonal prism. Daim duab hauv qab no qhia txog nws txoj kev loj hlob. Nws tuaj yeem pom tau tias thaj chaw xav tau yog tsim los ntawm ob lub pentagons zoo tib yam thiab tsib daim duab plaub sib npaug rau ib leeg.

Thaj chaw ntawm tag nrho cov saum npoo ntawm daim duab qhia los ntawm tus qauv:

S=2S_o+ 5S_p

Ntawm no cov ntsuas o thiab p txhais tau tias lub hauv paus thiab cov duab plaub, raws li. Cia peb qhia qhov ntev ntawm sab ntawm lub pentagon li a, thiab qhov siab ntawm daim duab li h. Tom qab ntawd rau lub duab plaub peb sau:

S_p=ah

Xaiv thaj tsam ntawm ib lub pentagon,siv tus qauv universal:

S=n/4a²ctg(pi/n)

Qhov twg n yog tus lej ntawm sab ntawm lub polygon. Hloov n=5, peb tau txais:

S₅=5/4a²ctg(pi/5) ≈ 1, 72a ²

Qhov tseeb ntawm qhov sib npaug yog 3 tus lej lej, uas txaus los daws txhua yam teeb meem.

Tam sim no nws tseem yuav pom qhov suav ntawm qhov tau txais thaj chaw ntawm lub hauv paus thiab sab saum npoo. Peb muaj:

S=21,72a² + 5ah=3, 44a² + 5a h

Nws yuav tsum nco ntsoov tias cov qauv tsim tau tsuas yog siv tau rau lub kaum sab xis. Nyob rau hauv cov ntaub ntawv ntawm ib tug oblique daim duab, qhov chaw ntawm nws lateral nto yog pom raws li kev paub ntawm lub perimeter ntawm txiav, uas yuav tsum tau perpendicular rau tag nrho cov parallelograms.

ntim ntawm daim duab

Cov mis rau xam qhov ntim ntawm lub pentagonal prism tsis txawv ntawm qhov kev qhia zoo sib xws rau lwm qhov prism lossis lub tog raj kheej. Qhov ntim ntawm ib daim duab yog sib npaug rau cov khoom ntawm nws qhov siab thiab thaj tsam ntawm lub hauv paus:

V=S_oh

Yog hais tias lub prism nyob rau hauv nqe lus nug yog lub duab plaub, ces nws qhov siab yog qhov ntev ntawm ntug tsim los ntawm cov duab plaub. Cov cheeb tsam ntawm lub pentagon tsis tu ncua tau suav nrog saum toj no nrog cov neeg siab. Hloov tus nqi no rau hauv cov mis rau ntim thiab tau txais cov lus qhia tsim nyog rau lub pentagonal prism tsis tu ncua:

V=1, 72a²h

Yog li, suav ntim thiab thaj chaw saum npooib txwm pentagonal prism yog ua tau yog tias sab ntawm lub hauv paus thiab qhov siab ntawm daim duab paub.