Area and volume of cuboid

A cuboid is a box-like shape. It has six rectangular faces. The faces opposite each other are equal.

volume

The volume of a cuboid = width × length × height

Remember that volume is measured in units cubed: mm³, cm³, m³ etc. 

Area

A cuboid can have two kinds of surface areas:

• Total Surface Area
• Lateral Surface Area

The total surface area of the cuboid is obtained by adding the area of each face while the lateral surface area of the cuboid is found by finding the area of each face excluding the base and the top. The total surface area is denoted by "S" while the lateral surface area is denoted by "L". The total surface area and lateral surface area can be expressed in terms of length (l), breadth(b), and height of cuboid(h) as:

Total Surface Area of Cuboid, S = 2 (lb + bh + lh)
Lateral Surface Area of Cuboid, L = 2h (l + b)

We can derive the formulas for the surface area of the cuboid by opening up a cuboid box. Let us see how.

To calculate the surface area of a cuboid you calculate the area of each face and add them together.

Remember that area is measured in units squared: mm², cm², m² etc.

. Calculate the volume of the wooden box:

1. Calculate the volume of the wooden box:

Volume = 20 × 35 × 15 = 10,500 cm³

2. Calculate the surface area by working out the area of each face and adding them together:

The area of the base = 35 × 20 = 700 cm²

The area of the top is the same = 700 cm²

The area of the front = 35 × 15 = 525 cm²

The area of the back is the same = 525 cm²

The area of the left = 15 × 20 = 300 cm²

The area of the right is the same = 300 cm²

Total surface area = (2 × 700) + (2 × 525) + (2 × 300) = 3,050 cm²

Difference between cube and cuboid 

Cube	Cuboid
Total Surface Area = 6(side)2	Total Surface area = 2 (Length x Breadth + breadth x height + Length x height)
Lateral Surface Area = 4 (Side)2	Lateral Surface area = 2 height(length + breadth)
Volume of cube = (Side)3	Volume of the cuboid = (length × breadth × height)
Diagonal of a cube = √3l	Diagonal of the cuboid =√( l2 + b2 +h2)
Perimeter of cube = 12 x side	Perimeter of cuboid = 4 (length + breadth + height)