Cuboid

Cuboid is a solid box whose every surface is a rectangle of same area or different areas.

A cuboid will have a length, breadth and height.

Hence we can conclude that volume is 3 dimensional. To measure the volumes we need to know the measure 3 sides.

Since volume involves 3 sides it is measured in cubic units.

$Units of Volume$

Volume of a cuboid = (length × breadth × height) cubic units.

= (l × b × h) cubic units.

(Since area = ℓ × b)

Volume of a cuboid = area of one surface × height cubic units

Let us look at the given cuboid.

The length of the cuboid = 5 cm

The breadth of the cuboid = 3 cm

The height of cuboid (thickness) = 2 cm

The number of 1 cm cubes in the given cuboid = 30 cubes = 5 × 3 × 2

We find that volume of the given cuboid with length 5 cm, breadth 3 cm and height 2 cm is 30 cu cm.

Therefore, volume of a cuboid = length × breadth × height

Solved examples on volume of a cuboid:

1. Find the volume of a cuboid of dimensions 14 cm × 12 cm × 8 cm.

Volume of cuboid = length × breadth × height.

Here, length = 14 cm, breadth = 12 cm and height = 8 cm.

Volume of cuboid = 14 × 12 × 8 cubic cm.

= 1344 cubic cm.

Therefore, volume of cuboid = 1344 cubic cm.

2. Find the volume of a cuboid of dimensions 14 cm × 50 mm × 10 cm.

Here, length = 14 cm,

[Given, breadth = 50 mm; we need to convert breadth to same unit and then solve. We know, 10 mm = 1 cm. Therefore, 50 mm = 50/10 cm = 5 cm].

Breadth = 5 cm,

Height = 10 cm.

Volume of cuboid = length × breadth × height.

= 14 × 5 × 10

= 700 cubic cm.

Therefore, volume of cuboid = 700 cubic cm.

Note: In a cuboid, when the length, breadth and height are of different units, convert them to a same unit and then solve.

3. Find the volume of a cuboid of dimensions 17 mm × 0.2 cm × 12 mm in cu. cm.

Given, length = 17 mm.

We know, 10 mm = 1 cm.

= 17/10 cm.

= 1.7 cm.

Therefore, length = 1.7 cm.

Similarly, height = 12 mm.

We know, 10 mm = 1 cm.

= 12/10 cm.

= 1.2 cm.

Therefore, height = 1.2 cm.

Volume of cuboid = length × breadth × height.

Length = 1.7 cm, breadth = 0.2 cm and height = 1.2 cm.

= 1.7 × 0.2 × 1.2 cu. cm.

= 0.408 cu. cm.

Therefore, volume of cuboid = 0.408 cubic cm.

4. Find the number of cubical boxes of cubical side 3 cm which can be accomodated in carton of dimensions 15 cm × 9 cm × 12 cm.

Volume of box = side × side × side.

= 3 × 3 × 3

= 27 cu. cm.

Volume of carton = length × breadth × height.

= 15 × 9 × 12

= 1620 cu. cm.

Number of boxes = Volume of carton/Volume of each box.

= 1620/27

= 60

Therefore, number of cubical boxes = 60.

5. How many bricks each 25 cm long, 10 cm wide and 7.5 cm thick will be required for a wall 20 m long, 2 m high and 0.75 m thick? If bricks sell at $900 per thousand what will it cost to build the wall?

Volume of the wall = 20 m × 2 m × 0.75 m

= 20 × 100 cm × 2 × 100 cm × 0.75 × 100 cm

Volume of brick = 25 cm × 10 cm × 7.5 cm

Number of bricks = Volume of the wall/Volume of the brick

= 20 × 100 × 2 × 100 × 0.75 × 100/25 × 10 × 7.5

= 16000

The number of bricks = 16000

The cost of 1 thousand bricks = $ 900

The cost of building the wall = $ 900 × 16 = $ 14400

Note: While calculating the volume of a cuboid all the dimensions should be changed into the same unit.

● Volume.

Units of Volume