Q6. - Algebra 2

Question

Twenty-seven white cubes of the same size are put together to form a larger cube. The larger cube is painted red. How many of the smaller cubes have exactly one red face?

(A) 4

(B) 6

(C) 9

(D) 12

Step-by-Step Solution

Answer

There are 12 smaller cubes that exactly have one red face.

Step 1 – Definition of cube

Cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five platonic solids. It has 6 faces, 12 edges, and 8 vertices.

Step 2 – Evaluate the number of small cubes required to make one side of large cube

Let  $a$ be the length of one side of cube.

Total number of white cubes = 27

$\begin{array}{c}a=\sqrt[3]{27}\\ =\sqrt[3]{3\times 3\times 3}\\ =3\end{array}$

3 smaller cubes are used to make one side of large cube.

Step 3 – Evaluate the number of cubes that exactly have one red face

There are 6 faces in a cube.

Therefore, the smaller cubes that exactly have one red face

$\begin{array}{c}=6\left(3\right)-3\left(2\right)\\ =18-6\\ =12\end{array}$