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Surface area of a Cube

Prisms are solids with plane faces. As we saw earlier, the surface area of prisms, i.e. the surface area of a solid with plane faces is the sum of the area of its faces.

We will first look at calculating the surface area of a cube, and then that of a rectangular prism and a triangular prism.

 

Surface area of a cube

A cube is a six-sided solid with a uniform cross-section; and the cross-section of a cube is a square.

Let us look at a cube with side 2 cm. ‘Opening up’ this cube will produce a net. A net is a flat diagram that contains the faces of a solid shape. The faces are arranged so that the diagram could be folded to form that solid (in this case, a cube). Drawing the net of a prism can help with calculating the surface area.

Surface area of a cube_1

So to calculate the surface area of this cube, we first calculate the area of one side.

Area of one side  =  2 x 2  =  4 cm2

Since there are six sides to a cube, Surface area of a cube = 6 x area of one face

=  6 x 4

=  24 cm2

In general, the formula to calculate the surface area of a cube, given side a, is –

Surface area of a cube = 6a2

 

Example 1 : What is the surface area of a cube with side 5 mm?

Let us first do a net diagram for this cube –

Surface area of a cube_2

Area of one face  =  5 x 5  =  25 mm2

Surface area of the cube  =  6 x area of one face

=  6 x 25

=  150 mm2

We can also calculate the surface area using the formula 6a2

Surface area  =  6 x 52

=  150 mm2

 

Example 2 : What is the surface area of a cube with side 7.5 m?

Surface area of a cube  =  6a2

=  6 x 7.52

=  6 x 56.25

=  337.5 m2

 

Here are some more examples of surface area of prisms.