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
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.