Surface Area of a Cube Formula

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 = l²

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

                                        = 6 × l² = 6l²

Surface area of a cube = 6l²  

 

Surface Area of a Cube Formula

 

Surface area of a cube = 6l²  

 

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 = l²

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

                                                          = 4 × l² = 4l²

Lateral surface area of a cube = 4l²

 

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 = 4l²

                                 = 4 × 5² = 4 × 25

                                 = 100 m²

Total surface area of a cube = 6l²

                                             = 6 × 5² = 6 × 25

                                                  = 150 m²

 

Example 2: The surface area of a closed cubical box is 600 cm². Find the edge of the

box.

 

Solution: We know that, the total surface area of a cubical box is given by A = 6l².

Therefore, 6l² = 600

l² = 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 = 6l²

                                             = 6 × (2.5)² = 6 × 6.25

                                             = 37.5 m²

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