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## What is the Total Surface Area of Cube?

The phrase “Total Surface” of simply “Surface” refers to the outer faces of any three-dimensional object. Therefore, the **Total Surface Area** (TSA) of a **Cube** may be defined as the sum of the **Area** of all six faces of the **Cube**.

To understand the concept of the **Total Surface Area** of a **Cube**, let us consider a **Cube** as shown in the figure below,

The **Cube** shown in the above figure has six faces (4 side faces, 1 top face and 1 bottom face). Since, it is a **Cube**, the length of all the edges are equal and denoted by the letter a. The **Total Surface Area** of the **Cube** will be the sum of the area of all six faces.

Area of one face,

A=a^2

Therefore, the Area of six faces,

TSA=6\times a^2

Which is the formula for finding TSA of cube.

## How to find the Total Surface Area of a Cube?

The **Total Surface Area** of the Cube can be found out from the Edge or the Lateral Surface Area of the cube. If any of the two are given, then, we can easily find the TSA of the Cube.

### Total Surface Area of Cube when the Edge is given

If the length of the edges of a cube, denoted by the letter a, is given, then, the formula for finding the **Total Surface Area (TSA)** of the cube is given by,

TSA=6a^2

### Total Surface Area of Cube when Lateral Surface Area is given

If the Lateral Surface Area of a Cube is given, then the **Total Surface Area** of the **cube** can be found out from the following relation,

LSA=\frac{2}{3}\times TSA

TSA=\frac{3}{2}\times LSA

## Solved Examples

**1. Find the total surface area of a cubic box if the length of the edge is 5cm?**

**Solution:** Given, the length of edge, a=5\,cm

The total surface area of the cubic box will be,

TSA=6\times a^2

TSA=6\times 5^2

TSA=6\times 25

TSA=150\,cm^2

**2. Reena wants to paint a cubical box for her school project. The edge of the box is 1.1 meter and the cost of painting per square meter is 50 Rs. Find the total cost for Painting the whole box?**

**Solution:** Given, edge, a=1.1\,m

The TSA of the box is,

TSA=6\times a^2

TSA=6\times (1.1)^2

TSA=6\times 1.21

TSA=7.26\,m^2

The cost of painting per square meter is 50 Rs. Therefore, the cost of painting the whole box,

=7.26\,m^2\times 50\,Rs.

=363 Rs.

## Frequently Asked Questions (FAQ)

**What is the difference between TSA and LSA?**

The main difference between TSA and LSA is that the TSA is the area of all the six faces of a cube, however, the LSA is the area of four side faces and does not include the top and the bottom faces.

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