The surface area or the total surface area of a cube is the entire space occupied by its outer faces. In other words, it is the number of unit squares needed to cover its shape. It is expressed in square units such as m^{2}, cm^{2}, mm^{2}, or in^{2}.

Formula

The formula is:

How to Find the Surface Area of a Cube

Let us understand how we consider the faces of a cube and calculate its surface area with a help of a net.

Since, the total surface area of a cube is the area of all its 6 faces, it includes the lateral surface area (LSA). LSA is the area of all faces, excluding the top and the base.

So, LSA = area of the four lateral or side faces

The formula is:

Lateral Surface Area (LSA) = 4a^{2}

Solved Examples

Find the surface area of a cube with side 5 cm.

Solution:

As we know, ∴ Surface Area (SA) = 6a^{2}, here a = 5 cm = 6 × 5^{2} = 150 cm^{2}

Calculate the lateral surface area of a cube with a side length of 9 mm.

Solution:

As we know, Lateral Surface Area (LSA) = 4a^{2}, here a = 9 mm = 4 × 9^{2} = 324 mm^{2}

Find the surface area of cubes with edges 4 cm and 8 in respectively.

Solution:

Here, the measure of two cubes is given. As we know, For one cube, Surface Area (SA) =6a^{2}, here a = 4 cm = 6 × 4^{2} = 96 cm^{2} For the other cube, Surface Area (SA) = 6a^{2}, here a = 8 in = 6 × 8^{2} = 384 in^{2}

How much marble paper will we need to cover a 6 cm cube-shaped gift box?

Solution:

As we know, The amount of marble paper needed is the surface area of a cube ∴ Surface Area (SA) = 6a^{2}, here a = 6 cm = 6 × 6^{2} = 216 cm^{2} So we will need 216 cm^{2} of marble paper to cover the whole cubical gift box.

Finding the Length of EDGE of the Cube when the SURFACE AREA is known

Find the side length of a cube whose area is 625 unit squares.

Solution:

As we know, SA = 6a^{2} ∴ ${a=\sqrt{\dfrac{SA}{6}}}$, here SA = 625 unit sq. ${\therefore a=\sqrt{\dfrac{625}{6}}}$ ≈ 10.21 units

Finding the SURFACE AREA of the cube when VOLUME is known

Calculate the surface area of a cube given its volume of 343 cm^{3}.

Solution:

Here, we will use an alternative formula. ${ SA=6V^{2/3}}$, here V = 343 cm^{3} ${\therefore SA=6\times \left( 343\right) ^{2/3}}$ = 294 cm^{2}