Question

A $3\times 3$ Rubik's cube has a total surface area of $54{\text{cm}}^2$. The area occupied by every single red tile of the cube is ___________ .

• A. $0.25{\text{cm}}^2$
• B. $1{\text{cm}}^2$
• C. $3{\text{cm}}^2$
• D. $9{\text{cm}}^2$

Answer 1

The correct option is B

$1{\text{cm}}^2$

Given,
Total surface area of the cube $=54{\text{cm}}^2$

We know that,
Cube has 6 number of faces.
Each face of the Rubik's cube contains 9 tiles.
Each Rubik's cube contains 9 red tiles.

$\therefore \text{Area of each face}$
$=\frac{\text{Total surface area of the cube}}{\text{Total number of faces of the cube}}=\frac{54}{6}=9{\text{cm}}^2$

Now, $\text{area of each tile}$
$=\frac{\text{Area of each face}}{\text{Total number of tiles in each face}}=\frac{9}{9}=1{\text{cm}}^2$

Hence, the area occupied by every single red tile of the cube is $1{\text{cm}}^2$.