Question

Alguém pode me explicar :
A razão entre as medidas das arestas de dois cubos é de 2 para 3. A aresta do cubo menor mede 3,6 cm.Determine:
a) A medida da aresta do cubo maior;
b) A razão entre as áreas de uma das faces do cubo menor e do cubo maior;
c) A razão entre os volumes do cubo menor e do cubo maior.

Answer 1

              Temos
                 Cubo 1 = C1
                 Cubo 2 = C2        [C2 > C1]
a)
                 (Aresta C1)/(Aresta C2) = 2/3 = (3,6)/(A2)
                                                                                      A2 = 5,4
b)
                  (Area C1)/(Area C2) = (Aresta C1)^2/(Aresta C2)^2
                                                   = (3,6)^2/(5,4)^2 = (12,96)/(29,16)
                                                   = 1/(2,25)
                                                                         (Area C1)/(Area C2) = 1/(2,25)
                                                                            Area C2 = 2,25 (Area C1)
                                                                  
c)
               Seguindo o mesmo raciocínio
                      (Volume C1)/(Volume C2) = (3,6)^3/(5,4)^3
                                                                = (16,656)/(157,464)
                                                                = 1/(9,4539)
                                                                        Volume C2= 9,4539 (Volume C1)