Volume of Cuboid

What is Cuboid?

A cuboid is a three-dimensional geometrical shape bounded by six rectangular faces. The opposite faces of cuboids are parallel and equal. It is also called a rectangular prism.

It has 6 faces, 8 vertices and 12 edges.

Examples of cuboid: Bricks, Duster, Books, etc

In this article, you will learn about the volume of cuboid, its formula and derivation along with some solved examples.

Volume of Cuboid

In geometry, the volume of any shape is the space occupied by it in a 3-dimensional space. So, the volume of a cuboid is defined as the space occupied by the cuboid in a three-dimensional space.

If the cuboid is hollow, then the amount of air or some liquid which can be stored in it is called the capacity of the cuboid. So, the capacity of cuboid is equal to the volume of cuboid.

The volume of cuboid having length ‘l’, breadth ‘b’ and height ‘h’ is given by the formula as below:

Volume of cuboid = l × b × h = lbh cubic units

Derivation of Volume of Cuboid

A cuboid can be seen as a set of rectangles having an area ‘A’ stacked on one other up to height ‘h’.

Measure of the space occupied by the stack of rectangles = the area of the plane region occupied by each rectangle × height.

So, we get:   volume of cuboid = A × h 

We know, area of rectangular region = A = l × b, putting this value in place of ‘A’ we get:

Volume of cuboid = l × b × h cubic units

Solved Examples: 

Q1. Find the Capacity of a Cuboidal Tank having Length 10m, Breadth 8m and Height 5m.

Solution: Given, the dimensions of the cuboidal tank are, length (l) = 10 m, breadth (b) = 8 m and height (h) = 5 m.

The capacity of cuboidal tank = volume of cuboidal tank = l × b × h cubic units

                                                                                     = 10 × 8 × 5 m3

                                                                                     = 400 m3

Therefore, the capacity of the cuboidal tank is 400m3.

Q2. Find the Cost of Digging a Cuboidal Pit 8m long, 5m Broad and 3m Deep at the Rate of  ₹25 per m3

Solution: Given, the dimensions of cuboidal pit are, length (l) = 8 m, breadth (b) = 5 m and depth (h) = 3m.

volume of cuboidal pit = l × b × h cubic units

                                      = 8 × 5 × 3 m3

                                      = 120 m3

Given that the cost of digging 1 m3 is25.

So, the cost of digging 120m3 = 120 × 25 = ₹3000

Therefore, the cost of digging a cuboidal pit is ₹3000.

Q3. How Many Bricks, Each of Size 24 cm × 12 cm × 8 cm will be Required to Build a Wall of Length 10 m, Breadth 24 cm and Height 5m?

Solution: 

Given, the dimensions of wall are, length (l) = 10 m = 1000 cm, 

                                                        breadth (b) = 24 cm and, 

                                                        height (h) = 5 m = 500 cm.

                So, the volume of wall = l × b × h cubic units

                                                        = 1000 × 24 × 500 cm3  

and, the dimensions of bricks are, length (l) = 24 cm, 

                                                        breadth (b) = 12 cm and, 

                                                         height (h) = 8 cm.

So, the volume of one brick = l × b × h cubic units

                                                   = 24 × 12 × 8 cm3  

Now, the number of bricks required =\[\frac{{Volume{\text{ }}of{\text{ }}wall}}{{Volume{\text{ }}of{\text{ }}brick}}\]

                                                           =\[\frac{{1000 \times 24 \times 500{\text{ }}cm3}}{{24 \times 12 \times 8{\text{ }}cm3}}\] = 5208.33 

Therefore, the number of bricks required to build the wall is 5209 bricks.