Sab nraub qaum ntawm lub khob hliav qab tsis tu ncua thiab truncated. Cov qauv thiab piv txwv ntawm kev daws qhov teeb meem

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

Thaum xav txog cov duab hauv qhov chaw, teeb meem feem ntau tshwm sim hauv kev txiav txim siab lawv thaj chaw. Ib daim duab zoo li no yog lub khob hliav qab. Xav txog hauv kab lus dab tsi yog sab saum npoo ntawm lub khob hliav qab nrog lub hauv paus puag ncig, nrog rau lub khob hliav qab.

Cone nrog puag ncig

Ua ntej yuav mus rau qhov kev txiav txim siab ntawm lub ntsej muag sab nraud ntawm lub khob hliav qab, peb yuav qhia seb nws zoo li cas thiab yuav ua li cas kom tau txais nws siv cov txheej txheem geometric.

Siv lub kaum sab xis ABC, qhov twg AB thiab AC yog ob txhais ceg. Cia peb muab daim duab peb sab no rau ntawm ceg AC thiab tig nws ncig ceg AB. Yog li ntawd, sab AC thiab BC piav txog ob qhov chaw ntawm daim duab hauv qab no.

Daim duab tau los ntawm kev sib hloov yog hu ua lub khob ncaj nraim. Nws yog puag ncig vim nws lub hauv paus yog lub voj voog, thiab ncaj vim tias ib qho perpendicular kos los ntawm sab saum toj ntawm daim duab (point B) cuam tshuam lub voj voog ntawm nws qhov chaw. Qhov ntev ntawm qhov perpendicular no hu ua qhov siab. Obviously, nws yog sib npaug rau ceg AB. Qhov siab yog feem ntau denoted los ntawm tsab ntawv h.

Dhau li ntawm qhov siab, lub khob ntsuas tau piav qhia los ntawm ob tus yam ntxwv ntxiv:

• generating, lossis generatrix (hypotenuse BC);
• puag ncig (ceg AC).

Lub vojvoog yuav raug sau los ntawm tsab ntawv r, thiab cov generatoratrix los ntawm g. Tom qab ntawd, coj mus rau hauv tus account Pythagorean theorem, peb tuaj yeem sau qhov sib npaug tseem ceeb rau daim duab hauv qab no:

g²=h²+ r²

Conical nto

Qhov tag nrho ntawm tag nrho cov generatrices tsim ib lub conical lossis lateral nto ntawm lub khob hliav qab. Nyob rau hauv tsos, nws yog ib qho nyuaj rau qhia uas lub tiaj tus duab nws sib raug rau. Cov tom kawg yog ib qho tseem ceeb kom paub thaum txiav txim siab thaj tsam ntawm lub conical nto. Txhawm rau daws qhov teeb meem no, siv txoj kev cheb. Nws muaj nyob rau hauv cov nram qab no: ib tug nto yog puas siab puas ntsws txiav raws li ib tug arbitrary generatrix, thiab ces nws yog unfolded rau lub dav hlau. Nrog rau txoj kev tau txais cheb, cov duab hauv qab no yog tsim.

Raws li koj tuaj yeem twv, lub voj voog sib raug rau lub hauv paus, tab sis lub voj voog yog ib qho conical nto, thaj chaw uas peb xav tau. Lub sector yog bounded los ntawm ob generatrices thiab ib tug arc. Qhov ntev ntawm lub tom kawg yog raws nraim sib npaug rau perimeter (ntev) ntawm lub voj voog ntawm lub hauv paus. Cov yam ntxwv no tshwj xeeb txiav txim siab tag nrho cov khoom ntawm lub voj voog ncig. Peb yuav tsis muab cov lej nruab nrab ntawm cov lej, tab sis tam sim ntawd sau cov qauv kawg, uas koj tuaj yeem xam qhov chaw ntawm lub lateral nto ntawm lub khob hliav qab. Tus qauv yog:

S_b=pigr

Thaj chaw ntawm qhov chaw conical S_byog sib npaug rau cov khoom ntawm ob qhov tsis muaj thiab Pi.

Lub khob hliav qab thiab nws nto

Yog tias peb nqa lub khob hliav qab thiab txiav nws sab saum toj nrog lub dav hlau sib luag, cov duab seem yuav yog lub khob hliav qab. Nws lateral nto yog txwv los ntawm ob puag ncig puag ncig. Cia peb qhia lawv cov radii li R thiab r. Peb qhia qhov siab ntawm daim duab los ntawm h, thiab generatrix los ntawm g. Hauv qab no yog daim ntawv txiav tawm rau daim duab no.

Nws tuaj yeem pom tau tias sab saum toj tsis yog lub voj voog, nws yog me dua hauv cheeb tsam, txij li qhov nruab nrab yog txiav tawm ntawm nws. Txoj kev loj hlob yog txwv rau plaub kab, ob ntawm lawv yog cov kab ncaj nraim-generators, ob qho tib si yog arcs nrog qhov ntev ntawm cov voj voog sib txuas ntawm lub hauv paus ntawm lub khob hliav qab.

Side deg S_b suav raws li hauv qab no:

S_b=pig(r + R)

Generatrix, radii thiab qhov siab yog cuam tshuam los ntawm kev sib npaug hauv qab no:

g²=h²+ (R - r)²

Qhov teeb meem nrog kev sib npaug ntawm thaj chaw ntawm cov duab

Muab lub khob hliav qab nrog qhov siab ntawm 20 cm thiab lub hauv paus vojvoog ntawm 8 cm. Nws yog ib qho tsim nyog yuav tsum nrhiav qhov siab ntawm lub khob hliav qab uas nws sab nraub qaum yuav muaj thaj tsam tib yam li lub khob hliav qab no. Daim duab truncated yog ua rau tib lub hauv paus, thiab lub vojvoog ntawm lub hauv paus sab saud yog 3 cm.

Ua ntej tshaj plaws, cia peb sau cov xwm txheej ntawm kev sib npaug ntawm thaj chaw ntawm lub khob hliav qab thiab daim duab truncated. Peb muaj:

S_b1=S_b2=>

pig₁R=pig₂(r + R)

Tam sim no cia peb sau cov kab lus rau cov generatrices ntawm txhua tus duab:

g₁=√(R²+ h₁²);

g₂=√((R-r)² + h₂ ²)

Siv g₁ thiab g₂ rau hauv cov qauv rau thaj tsam sib npaug thiab square sab laug thiab sab xis, peb tau txais:

R²(R²+ h₁²)=((R-r)²+ h₂²)(r + R)²

Peb tau txais cov lus qhia rau h₂:

h₂=√(R²(R²+ h 12^{)/(r + R)}2^{- (R - r)}2 ⁾

Peb yuav tsis ua kom yooj yim qhov kev sib npaug no, tab sis tsuas yog hloov cov ntaub ntawv paub los ntawm cov xwm txheej:

h₂=√(8²(8²+ 202^{)/(3 + 8)}2^{- (8 - 3)}2^{) ≈ 14.85 cm}

Yog li, txhawm rau kom sib npaug ntawm thaj chaw ntawm sab ntawm cov duab, lub khob hliav qab yuav tsum muaj qhov tsis muaj: R=8 cm, r=3 cm, h ₂≈ 14, 85 cm.