# The total surface area of a cube is 54\[c{{m}^{2}}\]. What is the length of its side?

Last updated date: 17th Mar 2023

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Hint:Cube has 6 faces,the total surface area of the cube is given.Find out the area of one face of the cube and next length of its side.

“Complete step-by-step answer:”

Given that the total surface area of the cube = 54\[c{{m}^{2}}\].

The surface area of a cube is \[6{{a}^{2}}\].

Where, a is the length of the side of each edge of the cube.

All the sides of the cube are equal.

\[\therefore \]a is the length of one side of the cube.

By looking at the figure, cube has six sides and each side is a square.

Length of the edge is a

\[\therefore \]Area of a square\[=a\times a={{a}^{2}}\]

Since, there are six sides, the total surface area is

Surface area\[={{a}^{2}}+{{a}^{2}}+{{a}^{2}}+{{a}^{2}}+{{a}^{2}}+{{a}^{2}}=6{{a}^{2}}\]

\[\therefore \]Surface area of cube is = \[6{{a}^{2}}\]

We have given the total surface area of cube = 54\[c{{m}^{2}}\].

\[\begin{align}

& \Rightarrow 6{{a}^{2}}=54 \\

& \therefore {{a}^{2}}=\dfrac{54}{6} \\

& \Rightarrow {{a}^{2}}=9 \\

& \therefore a=\sqrt{9}=3 \\

\end{align}\]

Length of its side = 3cm

Note: Cube has 6 faces, so the total surface area becomes \[6{{a}^{2}}\].

“Complete step-by-step answer:”

Given that the total surface area of the cube = 54\[c{{m}^{2}}\].

The surface area of a cube is \[6{{a}^{2}}\].

Where, a is the length of the side of each edge of the cube.

All the sides of the cube are equal.

\[\therefore \]a is the length of one side of the cube.

By looking at the figure, cube has six sides and each side is a square.

Length of the edge is a

\[\therefore \]Area of a square\[=a\times a={{a}^{2}}\]

Since, there are six sides, the total surface area is

Surface area\[={{a}^{2}}+{{a}^{2}}+{{a}^{2}}+{{a}^{2}}+{{a}^{2}}+{{a}^{2}}=6{{a}^{2}}\]

\[\therefore \]Surface area of cube is = \[6{{a}^{2}}\]

We have given the total surface area of cube = 54\[c{{m}^{2}}\].

\[\begin{align}

& \Rightarrow 6{{a}^{2}}=54 \\

& \therefore {{a}^{2}}=\dfrac{54}{6} \\

& \Rightarrow {{a}^{2}}=9 \\

& \therefore a=\sqrt{9}=3 \\

\end{align}\]

Length of its side = 3cm

Note: Cube has 6 faces, so the total surface area becomes \[6{{a}^{2}}\].

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