**Surface
Area of a Cube**

A cube is a three-dimensional (3D)
solid shape bounded by six square faces. A cube and its net is shown below. The
area of the net of the cube is called the surface area of the cube.

Let the
measure of each edge of the cube be *l*.

Area of each
square face of the net = *l*^{2}

Surface area
of the cube = Area of all six square faces

= 6
× *l*^{2} = 6*l*^{2}

Surface area of a cube = 6*l*^{2}

**Surface
Area of a Cube Formula**

**Surface
area of a cube = ****6 l^{2}**

**Lateral
Surface Area of a Cube Formula**

Lateral
surface area of a cube is equal to the area of the four lateral faces of the
cube.

Area of each
square face of the net = *l*^{2}

Lateral
surface area of the cube = Area of four lateral faces

= 4 × *l*^{2} = 4*l*^{2}

Lateral surface area of a cube = 4*l*^{2}

**Surface Area of a
Cube Example**

**Example 1: **Find the lateral
surface area and the total surface area of a cube, each of whose edge measures
5 m.

**Solution: **Given: edge, *l
*= 5 m

Lateral
surface area = 4*l*^{2}

= 4 × 5^{2}
= 4 × 25

= 100 m^{2}

Total
surface area of a cube = 6*l*^{2}

= 6 × 5^{2} = 6 × 25

= 150 m^{2}

**Example 2: **The
surface area of a closed cubical box is 600 cm^{2}. Find the edge of the

box.

**Solution: **We
know that, the total surface area of a cubical box is given by A = 6*l*^{2}.

Therefore, 6*l*^{2} = 600

*l*^{2} = 600/6 = 100

*l *=
10 cm

Thus, the edge of the box is 10 cm.

**Example 3: **Find the cost of making a wooden cubical box
of edge 2.5 m at the rate of Rs 100 per sq. m.

**Solution: **Given: edge of the cubical box, *l* = 2.5
m

Total
surface area of a cube = 6*l*^{2}

= 6 × (2.5)^{2} = 6 × 6.25

= 37.5 m^{2}

Cost of making the wooden box = Rs 100 × 37.5 = Rs 3750