# Total surface area of cube formula explained

Learn and know what is the formula of total surface area of cube in mensuration chapter. Regarding the cube T.S.A is one of the important formulas we compulsorily should learn.

First know what is a cube meaning according to geometry. We generally say the 3D shape of a square is called as a cube. For a cube there are mainly 4 formulas to learn. They are volume of cube, lateral surface area of cube (L.S.A), total surface area of cube (T.S.A) and the last one is formula of diagonal of a cube. Now we learn the formula for calculating the total surface area of a cube.

## What does total surface area (T.S.A) of a cube means?

We all know that cube contains 6 square faces. All these 6 square faces areas, if we find out and add them the result is called as total surface area of cube. In a simple way total surface area of cube means sum of 6 faces.

### The formula for the total surface area of cube as follows:

Consider a cube of length “k” units. Then the formula for finding T.S.A of cube i.e. total surface area of cube is given by 6${ k }^{ 2 }$ square units.

Examples:

What is total surface area (T.S.A) of a cube which has 5 cm length?

Solution:

Given,

Length of a cube is 5 cm i.e. k = 5cm.

We know that, the total surface area (T.S.A) of cube = 6${ k }^{ 2 }$ = 6 × ${ 5 }^{ 2 }$ = 6 × 25 = 150 square cm.

The T.S.A of a cube is given as 54 sq.m then what is the side of a cube?

Solution:

Given

6${ k }^{ 2 }$ = 54

${ k }^{ 2 }$ = $\frac { 54 }{ 6 }$

${ k }^{ 2 }$ = 9

K = +3 or -3

K = -3 is not possible, so k = 3 i.e. side of cube is 3 m.

If the length is 6 cm then what is T.S.A of a cube?

Solution:

Given

K =6 cm.

T.S.A of a cube = 6 × ${ 6 }^{ 2 }$ = 6 × 36 = 216 sq.cm

The T.S.A of a cube is 384 square units, then what is the base area of a cube?

Solution:

Given

T.S.A of a cube = 384 sq.units

6${ k }^{ 2 }$ = 384

${ k }^{ 2 }$ = 384/6

${ k }^{ 2 }$ = 64

K = -8 or +8.

As k = -8 is not possible, so take k = 8 units.

The base of a cube will be in the shape of a square. So we need to area of square. Therefore area of base = 8 × 8 = 64 sq.units.