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Corpuri geometrice-Arii si volume

Corpuri geometrice-Arii si volume. Prisma(cubul, paralelipipedul), Piramida, Trunchi de piramida Profesor: Doina Paun Grupa a IV- a Bulboaca Mircea Hartegan Dragos, Scurtu Bogdan, Tudor Ovidiu. Cubul & paralelipipedul. PARALELIPIPED

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Corpuri geometrice-Arii si volume

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  1. Corpurigeometrice-Ariisi volume Prisma(cubul, paralelipipedul), Piramida, Trunchi de piramida Profesor: Doina Paun Grupa a IV- a Bulboaca Mircea Hartegan Dragos, Scurtu Bogdan, Tudor Ovidiu

  2. Cubul & paralelipipedul PARALELIPIPED • CUBUL I H I H F G F D C D C G A B A B

  3. Piramidapatrulateraregulata & prismapatrulateraregulata PIRAMIDA PATRULATERA REGULATA I H V F G D C D C T A B A B PRISMA PATRULATERA REGULATA

  4. Prisma-cubul Cubulestepoliedrul care are toatefetelepatrate . V cub =Ab * h, undeAb=aria bazei Ab = l*l 1 l=h 2 Din 1 si 2 => Vcub = l3 At = Al + Abt1 At = arietotala, Al = arielaterala, Abt = ariebazatotala Al = Af * 4 , Af = l*l 2Af = aria unei fete Ab t = Ab * 2, Ab = l*l 3Ab = aria uneibaze Din 1, 2 si 3 => At = 6 * l Fie cubul ABCDFGHI AC =l√21 CH = l 2 ABH= triunghidreptunghic3 Din 1 2 si 3 + TeoremaluiPitagora => AH = l√3 diagonalacubului = l√3 bf

  5. Prisma- Paralelipiped Paralelipipedulestepoliedrul care are bazeledreptunghiuri. V= Ab * h 1Ab = aria bazei Ab = L*l 2 Din 1 si 2 => V= L*l*h At = 2(A1 + A2 + A3 ) 1 At = arietotala, A1 = arie fete laterale, A2 = ariebazatotala A3 = arie fete laterale A1 = L*l A2 = l*h A3 = L*h => At = 2(L*l + l*h + L*h) Fie paralelipipedul ABCDFGHI ABC – dreptunghic in B  (T.P) AC= AB2 + BC2 ACH – dreptunghic in C  (T.P) AH= AB2 + BC2 + CH2 diagonalaparalelipipedului= l2 + L2 + h2

  6. Piramida-regulata Poliedrul cu baza poligon regulat si muchiile laterale respectiv congruente se numeste piramida regulata. Inaltimea unei piramide “cade” in centrul bazei. Orice piramida triunghiulara se numeste tetraedru. Inaltimea unei fete laterale se numeste apotema piramidei. Formule ( piramida patrulatera regulata) At = Al + Ab 1 At = aria totala Al = aria laterala Ab = aria bazei Al = 4 * Af Af = ap * lb ap – apotema piramidei lb – latura bazei Al = ap * 4* lb 2 Ab = l* l 3 Din 1 2 si 3 => At = l2 + ap * 4* lb Volumul unui tetraedru este un numar egal cu o treime din produsul dintre aria unei fete oarecare si inaltimea corespunzatoare ei. Volumulpiramidei = Ab * h /3 h= inaltimea piramidei

  7. Trunchi de piramida Prin sectionarea unei piramide cu un paln paralel cu baza se obtine o piramida asemenea cu piramdia initiala si un trunchi de piramida, iar sectiunea obtinuta va fi un poligon asemenea cu baza piramidei. Elementele unui trunchi de piramida: - doua baze(poligoane asemenea) - fetele laterale sunt trapeze Trunchi de piramida provenit dintr-o piramida regulata se va numi trunchi de piramida regulata. Trunchi de piramida cu baza patrat At = Ab.m ari + Al + Ab.mici Abazei mari = L2 A bazeimici = l2 A l = 4* L*l At = 4* L*l + L2 + l2 Vtrunchi de piramida = h · (L + l + AB · Ab) / 3

  8. Multumimpetnruvizionare

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