### Cuboid

A cuboid is a three-dimensional shape has six, rectangle-shaped sides. Cuboid also have eight vertices (corners) and twelve edges. The angles in a cuboid are all right angles.

### Face Diagonals:

Face diagonals are line segments linking the opposite corners of a face. Each face has two, for a total of 12 in the cuboid. The length of the face diagonals is given by the formula

Length of Diagonal of Face of the Cuboid = √(length^{2} + breadth^{2} )

### Space Diagonals:

Space diagonals are line segments linking the opposite corners of a cuboid, cutting through its interior. A cuboid has 4 space diagonals. The length of the space diagonal is given by the formula

Length of Diagonal of Cuboid = √(length^{2} + breadth^{2} + height^{2})

### Perimeter:

The perimeter of a cuboid found by adding all the sides.

Perimeter = 4(length + breadth + height)

### Example:

If the length, width and height of a cuboid are 5 cm, 3 cm and 2 cm, find its Perimeter.

### Solution:

Perimeter = 4 (5+3+2)

P = 4 (10)

P = 40 cm

### Volume:

The volume of the cuboid is equal to the product of the area of one surface and height. Volume is measured in cubes (or cubic units)

Volume = length × breadth × height

### Example:

If the length, breadth and height of a cuboid are 5 cm, 2 cm and 4 cm, then find its volume.

### Solution:

V = 5 x 2 x 4

V = 40 cubic cm

### Surface Area:

Sum of the areas of all its 6 rectangular faces

Surface Area = 2(lb + bh +lh)

### Example:

The length, width and height of a cuboid are 11cm, 9cm and 15cm respectively. Calculate the total surface area of the cuboid.

### Solution:

TSA = 2 (11*9 + 9*15 + 15*11)

= 2(99 + 135 + 165)

= 2 * 399

TSA = 798cm²

### Lateral surface:

The sum of surface areas of all sides except the top and bottom face of solid is defined as the lateral surface area of a solid.

Lateral surface = 2h(l +b)

Where, l is lenght, b is breadth, h is height

### Example:

If the length, breadth and height of a cuboid are 5 cm, 3 cm and 4 cm, then find its lateral surface area.

### Solution:

LSA = 2h(l+b)

= 2 x 4(5+3)

= 2 x 4(8)

LSA = 2 x 32 = 64 cm^{2}

### Properties of Cuboid:

- It has 12 edges
- It has 8 corners or vertices
- It has 6 faces.
- All faces of the cuboid are in a rectangle shape.
- The angles in a cuboid are all right angles
- The edges opposite to each other are parallel.