# Cuboid (Definition, Shape, Perimeter, LSA, TSA, Volume)

## What is a Cuboid?

We know that a Rectangle is a two-dimensional shape in which two pairs of opposite sides are parallel to each other, and the lengths of these parallel sides are the same, as shown in the figure below. Since the Rectangle is a two-dimensional object, it has two dimensions, called Length and Breadth, as shown in the figure below. Now, if another dimension called height is added to the rectangle then the resulting three-dimensional shape is called Cuboid. The shape of Cuboid, Surface Area of Cuboid, Perimeter of Cuboid, Volume of Cuboid etc. are discussed below.

## Cuboid Shape

If we stack some rectangular sheets of the same size as shown in the figure below, we will get a box-like structure. This box-like structure is called a Cuboid. Since the Cuboid is composed of rectangular pieces stacked up to a particular height, it will have another dimension called Height, as shown in the figure below.

Now, let’s cut the edges of the Cuboid and open its six faces as shown in the figure below.

From the figure, it is clear that, all the six faces are of Rectangular shape. Therefore the area of each faces is given by,

Area of face 1, $A_1=l\times b$

Area of face 2, $A_2=b\times h$

Area of face 3, $A_3=l\times h$

Area of face 4, $A_4=b\times h$

Area of face 5, $A_5=l\times b$

Area of face 6, $A_6=l\times h$

## Total Surface Area of cuboid

The Total Surface Area of Cuboid or simply the Surface Area of Cuboid may be defined as the sum of the area of all the six faces of the Cuboid. Therefore,

Total Surface Area, $TSA=A_1+A_2+A_3+A_4+A_5+A_6$

$\Rightarrow\,\,TSA=(l\times b)+(b\times h)+(l\times h)+(b\times h)+(l\times b)+(l\times h)$

$\Rightarrow\,\,TSA=(2\times l\times b)+(2\times b\times h)+(2\times h\times l)$

$\Rightarrow\,\,TSA=2(lb+bh+hl)$

The above is the formula of Total Surface Area of Cuboid or simply the Surface Area of Cuboid where, $l$ is the length, $b$ is the breadth and $h$ is the height of the Cuboid.

## Lateral Surface Area of Cuboid

If out of the six faces of the Cuboid as shown in the above figure, if we only calculate the area of the four faces which are at the sides, leaving the top and bottom face, then the result is called the Lateral Surface Area of Cuboid. Therefore, the Lateral Surface Area of the Cuboid will be,

Lateral Surface Area, $LSA=A_2+A_3+A_4+A_6$

$\Rightarrow\,\,LSA=(b\times h)+(l\times h)+(b\times h)+(l\times h)$

$\Rightarrow\,\,LSA=(2\times l\times h)+(2\times b\times h)$

$\Rightarrow\,\,LSA=2h(l+b)$

The above is the formula of Lateral Surface Area of Cuboid, where, $l$ is the length and $b$ is the breadth of the Cuboid.

## Relation between Total Surface Area and Lateral Surface Area of Cuboid

The Total Surface Area of Cuboid is given by,

$TSA=2(lb+bh+hl)$

$TSA=2lb+2bh+2hl$

And, the Lateral Surface Area of Cuboid is given by,

$LSA=2h(l+b)$

$LSA=2bh+2hl$

Therefore,

$TSA=2lb+LSA$

Or,

$LSA=TSA-2lb$

## Perimeter of Cuboid Formula

The Perimeter of Cuboid may be defined as the sum of the length of all the edges. Therefore, the formula for finding the Perimeter of Cuboid is given by,

$P=4(l+b+h)$

Where, $l$ is the length, $b$ is the breadth and $h$ is the height of the Cuboid.

## Volume of Cuboid Formula

The formula for finding the Volume of Cuboid is given by,

$V=l\times b \times h$

Where, $l$ is the length, $b$ is the breadth and $h$ is the height of the Cuboid.

## Difference between Cube and Cuboid

The differences between Cube and Cuboid are tabulated below:

### What is a cuboid?

A Cuboid may be defined as a three-dimensional shape that is made up of stacking rectangular sheets. The three dimensions of a cube are Length, Breadth and Height.

### What is lateral surface area of cuboid?

The Lateral Surface Area of Cuboid is the area of the four side faces leaving the top and the bottom face.

### How many faces does a cuboid have?

A Cuboid has 6(six) faces.

### How many edges does a cuboid have?

A Cuboid has 12 edges.

### How many corners does a cuboid have?

A cuboid has 8 corners and these corners are called the vertices.

### What is the difference between cube and cuboid?

The difference between a cube and a cuboid is that all edges of a cube have the same length, or it can be said that the length, breadth and height of the cube are equal. However, in the case of a cuboid, the edges are or it has different length, width, and height.