Question

There are 20 unit cubes all of whose faces are white, and 44 unit cubes all of whose faces are red. They are put together to form a bigger cube (4 $\times$ 4 $\times$ 4). What is the minimum number of white faces Visible on this larger cube?

• A. 20
• B. 14
• C. 12
• D. 8

Answer 1

Answer: (C)

12

Given 4 $\times$ 4 $\times$ 4 cubes is mode faces 64
1 $\times$ 1 $\times$ 1 cubes
total cubes = 64, white = 20, Red = 44
To find minimum number of visible white box
Counting total visible faces of unit cube
Total number of faces of small cube on bigger cube
except boundry cubes = 4 $\times$ 6 =24
Counting boundry cube = 16 + 8 + 8 = 32
$\therefore$ Totalvisiblefaces = 56
But we have 44 Red cube
$\therefore$ minimum of number of white faces cubes which are visible = 56 - 44 = 12