Question

: The perimeter of one face of a cube is 24 cm. Find the total area of the 6 faces in \[{\text{c}}{{\text{m}}^2}\]

Answer 1

Hint: Since each side of the cube is square, calculate the length of the square using the given perimeter by equating $4\left( {{\text{side}}} \right)$ to 24 . Then, use the side of the square to find its area. Multiply the area of one face of the cube by 6 to find the total area of 6 faces.

Complete step-by-step answer:
Since, each face of a cube is square.
Let each side of the cube $a$.
Then, perimeter of one face is given by $4a$
We are given that the perimeter of one face of the cube is 24 cm.
Hence, we can write it as, $4a = 24$
On solving it, we get $a = 6$
That is, each side of the cube is 6 cm.
Now, we will find the area of one face of the cube.
Area of cube is given by, ${\text{side}} \times {\text{side}}$
Thus, the area of one face of given cube $6 \times 6 = 36{\text{ c}}{{\text{m}}^2}$
Multiply the area of one face of the cube by 6 to find the total area of 6 faces.
Therefore, the area of 6 faces is $36 \times 6 = 216{\text{ c}}{{\text{m}}^2}$
Hence, the total area of the 6 faces in \[{\text{c}}{{\text{m}}^2}\] is $216{\text{ c}}{{\text{m}}^2}$.

Note: Area of cube is given by, ${\text{side}} \times {\text{side}}$. The area of six faces of the cube is also known as total surface area and is calculated using the formula, ${\text{6}}{\left( {{\text{side}}} \right)^2}$. Hence, this question can alternatively be done by using the formula of total surface area of cube.