Formula for Volume of Cuboid – Derivation and Examples

Here you will learn what is the formula for volume of cuboid, its derivation and examples.

Let’s begin –

Formula for Volume of Cuboid

suppose, the length of cuboid is l, breadth of cuboid is b and height of cuboid is h. Then

Volume of Cuboid = l \(\times\) b \(\times\) h

Also Read : Formula for Surface Area of Cuboid – Derivation & Examples

Derivation :

Let the area of each rectangle is A, the height up to which the rectangles are stacked is h and the volume of the cuboid is V.

The relationship between the volume and area is given by the formula,

V = A \(\times\) h

\(\implies\) V = l \(\times\) b \(\times\) h

where l is the length and b is the breadth of rectangle. So, its area is l \(\times\) b.

Example : A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12 cm × 8 cm, how many bricks would be required? 

Solution : Since the wall with all the bricks makes up the space occupied by it, we need to find the volume of the wall, which is nothing but a cuboid.

Here, Length of Cuboid = 10 m = 1000 cm

Thickness(breadth) = 24 cm

Height = 4 m = 400 cm

Therefore, Volume of the wall(Cuboid) = length × thickness × height

= 1000 × 24 × 400 \(cm^3\)

Now, each brick is a cuboid of length = 24 cm, breadth = 12 cm and height = 8 cm

So, volume of each brick = length × breadth × height = 24 × 12 × 8 \(cm^3\)

So, number of bricks required = volume of the wall/volume of each brick

= \(1000 × 24 × 400\over 24 × 12 × 8\) = 4166.6

So, the wall requires 4167 bricks.