Question

The perimeter of one face of a cube is $24{\text{ cm}}$. Find the total area of the $6$ faces in ${\text{cm}}$.

Answer 1

We have given the perimeter of the side of the cube and we have to calculate the area of six faces of the cube. So, firstly we have to calculate the side of the face of the cube. This side will also be the side length of the cube then we have to find an area of six faces. This area will be equal to the area of the cube. We can apply the formula of the area of the cube. This will lead us to the required result.

Complete answer:
We have given that perimeter of one face of $cube = 24cm$. We have calculated the total area of $6$ faces. We know that each face of the cube is a square.
Let each side of the square $'a'$ perimeter of the square is equal to $24cm$ . We also know that the perimeter of the square is given as $4 \times side = 4 \times a$.
So $4a$ is equal to $24cm.$
$a$ will be equal to $\dfrac{{24}}{4} = 6.$
$a$ will be equal to $6cm.$
side of square $= {\text{ }}6cm$
Now, the area of $6$ faces will be equal to the area of the cube.
And area of cube is given as $6 \times {(side)^2}$
So, the area of the six faces of the cube will be equal to$6 \times {(side)^2}$.
$= 6 \times {(6)^2}$
$= 6 \times 6 \times 6{\text{ = }}216{\text{ c}}{{\text{m}}^2}$

Therefore, area of six faces of cube $= 216c{m^2}$

Note: Cube is a three dimensional structure in which each side of the structure is a square. It has six faces, twelve edges and eight vertices. Area of the quantity that expresses the extent of a two-dimensional figure. It can be said that the area of unit squares that cover the surface of a close figure.