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.

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