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eCursuri » Cursuri online » eScoala » Geometrie in spatiu - arii si volume » Lectia 1
Cubul
518711 afisari

Formule utile

cursuri

diagonala bazei = l · √2
diagonala cubului = l · √3

Desenarea corecta a unui cub

icon tutorialeAtunci cand vrei sa desenezi o figura geometrica, foloseste intotdeauna rigla si creionul. Obisnuieste-te sa faci figurile geometrice cat mai mari pentru a-ti fi mai usor atunci cand va trebui sa urmaresti in cadrul lor diverse puncte, unghiuri sau segmente.

1 Deseneaza un patrat cu o latura, de exemplu, de 8 cm:
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2 Dupa ce ai desenat patratul, din centrul acestuia mai deseneaza catre partea dreapta, inca un patrat cu latura egala cu latura primului patrat:
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3 Uneste cu cate o linie varfurile celor doua patrate:
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4 In cele din urma, sterge putin cate putin, cu guma, liniile care nu ar trebui sa se vada in spatiu. Vei obtine in final urmatoarea figura geometrica:
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Exercitii rezolvate

1. Calculeaza aria laterala, aria totala si volumul unui cub cu latura de 3 cm.
Rezolvare:
Aria laterala a cubului = 4 · l² = 4 · 3² = 36 cm²
Aria totala a cubului = 6 · l² = 6 · 3² = 54 cm²
Volumul cubului = l³ = 3³ = 27 cm³

2. Afla volumul si aria totala a unui cub care are suma muchiilor de 48 cm.
Rezolvare:
Suma muchiilor unui cub = 12 · l = 48 cm. Deci latura va fi de 4 cm.
Volumul cubului = l³ = 4³ = 64 cm³
Aria totala a cubului = 6 · l² = 6 · 4² = 96 cm²

3. Un cub are diagonala de 2√3 cm. Calculeaza cat este aria laterala, aria totala a cubului.
Rezolvare:
Diagonala cubului = l · √3 = 2 · √3 cm. Deci latura cubului va fi 2 cm.
Aria laterala a cubului = 4 · l² = 4 · 2² = 16 cm²
Aria totala a cubului = 6 · l² = 6 · 2² = 24 cm²
Volumul cubului = l³ = 2³ = 8 cm³

4. Volumul unui cub este de 125 cm³. Sa se calculeze aria bazei, aria laterala si aria totala a cubului.
Rezolvare:
Volumul cubului = l³ = 125 cm³. De aici rezulta ca latura cubului este de 5 cm.
Aria bazei cubului = l² = 5² = 25 cm²
Aria laterala a cubului = 4 · l² = 4 · 5² = 100 cm²
Aria totala a cubului = 6 · l² = 6 · 5² = 150 cm²

5. Daca aria totala a unui cub este 24 cm², sa se afle cat este aria laterala si volumul cubului.
Rezolvare:
Aria totala a cubului = 6 · l² = 24 cm², adica latura cubului este 2 cm.
Aria laterala a cubului = 4 · l² = 4 · 2² = 16 cm²
Volumul cubului = l³ = 2³ = 8 cm³
Paralelipipedul dreptunghic »
27 comentarii
ADRYANA29 25 august 2011, 13:29 1
faptul ca aratati cum tb desenat este f util. va rog sa puneti si aici functia de imprimare.
multumesc
  62    Raspunde
admin 25 august 2011, 13:51 2
@ADRYANA29: Este functia de printare. Trebuie doar sa te loghezi (e in partea de sus ca si la restul lectiilor sau tutorialelor)
  55    Raspunde
antonela 13 septembrie 2011, 11:04 3
am fiica in clasa a VIII-a; mi-a placut matematica si o ajut cu mare placere, iar aceste prezentari sunt foarte utile. multumesc!
  105    Raspunde
Anysuka 20 septembrie 2011, 20:29 4
cum se deseneaza un cub e fascinant..cu desenul nu e punctu meu forte...deci geometrie...nu mai zik..
  28    Raspunde
corny 24 noiembrie 2011, 21:43 5
foarte educativ...multumiri.
  31    Raspunde
dannitopa 11 decembrie 2011, 07:32 6
Sunt necesare si cateva probleme , prezentate gradual din punct de vedere al dificultatii de rezolvare . In felul acesta se pot vedea care sunt aptitudinile sau dificultatile la invatarea geometriei . Elevul trebuie sa stie ca studiul matematicii are doua componente :
- insusirea corecta a toeriei
- antrenamentul pentru rezolvarea problemelor de mate cu grad de dificultate din ce in ce mai mare .
  5    Raspunde
dannitopa 11 decembrie 2011, 07:37 7
Scuzati , in comentariul anterior am uitat sa fac o precizare . Problemele de mate la care fac referire ar trebui prezentate fara rezolvare .Cei interesati sa incerce sa le rezolve si apoi sa prezinte rezolvarile in comentarii .
  14    Raspunde
Denis.Rosu 20 aprilie 2012, 13:29 8
E foarte folositor :)
  7    Raspunde
buruianaizabela 04 mai 2012, 14:10 9
e foate interezant acest curs,si foarte util
  1    Raspunde
cainele_curaj 22 iunie 2012, 12:29 10
e foarte simplu nu prea te ajuta
  -70    Raspunde
c.ronaldo97 26 iunie 2012, 20:10 11
Aceste prezentari sunt foarte bune....Eu maine am examen la matematica si ma mai uit prin ele asa sa imi mai amintesc cate ceva...mai zic odata foaarte bune prezentarile;)
  24    Raspunde
Electronic 15 februarie 2013, 14:18 12
Am o intrebare
Am o problema si imi spune sa aflu lungimea muchiei cubului cum o aflu ??
  -16    Raspunde
Knight_Of_Glory 03 martie 2013, 17:24 13
@Electronic: muchia este latura in cub :)
  -7    Raspunde
XanderNight 22 februarie 2013, 11:50 14
Ati uitat diagonala cubului
d=l√3
  -6    Raspunde
Knight_Of_Glory 03 martie 2013, 17:25 15
foarte ajutator dar ar mai fi nevoie de probleme demonstrate...
  0    Raspunde
AnaDen 26 iunie 2013, 17:28 16
Este folositor .. dar de ce nu apare si rombul ?
  -3    Raspunde
Ionut06 20 iunie 2015, 14:55 17
Scrie aici comentariul tau
  0    Raspunde
Cristi12341 02 aprilie 2017, 17:57 18
Foarte folositor acest site, multumesc! :*
  0    Raspunde
TEEMO09 05 mai 2017, 09:42 19
Ati uitat diagonala cubului L√3 si a patratului L√2
  0    Raspunde
TEEMO09 05 mai 2017, 09:43 20
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  0    Raspunde
TEEMO09 05 mai 2017, 09:43 21
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TEEMO09 05 mai 2017, 09:43 22
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  0    Raspunde
TEEMO09 05 mai 2017, 09:43 23
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  0    Raspunde
TEEMO09 05 mai 2017, 09:43 24
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  0    Raspunde
TEEMO09 05 mai 2017, 09:43 25
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TEEMO09 05 mai 2017, 09:43 26
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  0    Raspunde
TEEMO09 05 mai 2017, 09:43 27
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Cuprinsul cursului
1. Cubul
2. Paralelipipedul dreptunghic
3. Prisma triunghiulara
4. Prisma patrulatera
5. Prisma hexagonala
6. Piramida triunghiulara
7. Piramida patrulatera
8. Piramida hexagonala
9. Trunchiul de piramida triunghiulara
10. Trunchiul de piramida patrulatera
11. Trunchiul de piramida hexagonala
12. Cilindrul
13. Conul
14. Trunchiul de con
15. Sfera
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