# Volume of Cuboid || Volume of Cuboid Formula

## What is Cuboid?

Its a 3 D shape of a rectangle

Cuboid has six rectangle faces, 8 vertices and 12 edges

Features of Cuboid
(a) Its a 3D Rectangle
(b) has six rectangle faces
(c) All angles measure 90 degree

Example of Cuboid

Construction bricks are the most common example of cuboid in daily life

## What is Volume of cuboid?

Volume of cuboid is the amount of space captured inside the cuboid

Given above is the cuboid glass vessel

Do you know how much volume of water needed to fill the vessel to brim?

It is the volume of the cuboid vessel.
Hence the amount of space captured in whole is the volume of the vessel

Currently, the vessel is filled with air but the vessel space can be utilized to store water.

## Volume of Cuboid Formula

The Formula for volume of cuboid is given as:

Volume = Length x Height x Breadth

## Volume of Cuboid – Formula Explanation

We know that cuboid is made of 6 rectangle faces joined together at 90 degrees.

The formula for cuboid volume is derived from this rectangular structural property of cuboid

We have seen that volume of cuboid;

Volume = Length x Height x Width

We will understand the formula built-up step by step

Step 01
Multiply Length x Height

Length x Height multiplication finds area of one rectangular face

Step 02
Including Breadth in the multiplication opens third dimension

Volume = Length x Breadth x Height

Hence the above formula covers the three dimension of cuboid and finds the volume

## Unit of Volume

The volume of cuboid is measured in cubic unit

Given above is the cuboid with dimension

The volume is calculated as:

Volume = Length x Height x Breadth

\mathtt{Volume\ =\ 4\ cm\ \ \times \ 2\ cm\ \times 1\ cm\ }\\\ \\ \mathtt{Volume\ =\ 8\ cm^{3}}

Observe that cubic unit \mathtt{cm^{3}} is used to represent volume of cuboid.

## Volume of Cuboid Questions

(01) Find the volume of cuboid with length = 8 cm, breadth = 3 cm and height = 5 cm

Given
Length of cuboid = 8 cm
Breadth of cuboid = 3 cm
Height = 5 cm

Volume of Cuboid = Length x Breadth x Height

\mathtt{Volume\ =\ 8\ cm\ \ \times \ 3\ cm\ \times 5\ cm\ }\\\ \\ \mathtt{Volume\ =\ 120\ cm^{3}}

Hence 120 \mathtt{cm^{3}} is the solution

(02) Given below is the cuboid aquarium
Find the volume of water needed to fill the aquarium fully

Given
The aquarium is in the form of cuboid

Length = 60 cm
Width = 30 cm
Height = 40 cm

Volume of Cuboid = Length x width x Height

\mathtt{Volume\ =\ 60\ \times \ 30\ \times \ 40\ cm^{3}}\\\ \\ \mathtt{Volume\ =\ 72000\ cm^{3}}

Hence, 72000 cu. cm of water is needed to fill the aquarium

(03) Given below is the dimension of cuboid in Millimeter (mm)
Find the volume in cubic centimeter

Given:
Length = 50 mm
Width = 20 mm
Height = 40 mm

Since we have to find volume in cu. cm, convert the data from mm to cm

we know that:
1 mm = 0.1 cm

So,
Length = 50 mm = 5 cm
Width = 20 mm = 2 cm
Height = 40 mm = 4 cm

Volume of cuboid = Length x Width x Height

\mathtt{Volume\ =\ 5\ \times \ 2\ \times \ 4\ cm^{3}}\\\ \\ \mathtt{Volume\ =\ 40\ cm^{3}}

Hence, 40 cu cm is the solution

(04) A cuboid box of length = 100 cm, width = 200 cm and height 150 cm is available for packing purpose.
Find how many box of dimension, 10 cm x 5 cm x 4 cm can be packed inside the big box

Given:
Dimension of big box
Length = 100 cm
Width = 200 cm
Height = 150 cm

Volume of big box = 100 x 200 x 150 cu. cm

Volume (V1) = 30,00,000 cubic cm

Dimension of small box
Length = 10 cm
Width = 5 cm
Height = 4 cm

Volume of Small Box (V2) = 10 x 5 x 4

Volume (V2) = 200 cubic cm

Number of small box that can accommodate inside big box = V1 / V2

\mathtt{Number\ =\ \frac{Volume\ of\ big\ box\ ( V1)}{Volume\ of\ small\ box\ ( V2)}}\\\ \\ \mathtt{Number\ =\ \frac{30,00,000}{200}}\\\ \\ \mathtt{Number\ =\ 15,000\ boxes}

Hence, there 15,000 small box can be packed inside the large one

(05) A cuboid wall has to be made of dimension 2.5 meter x 0.4 meter x 1.5 meter.
The bricks used for construction has dimension 5 cm x 10 cm x 2.5 cm . Find the number of bricks used in wall construction

Dimension of wall given:
Length = 2.5 meter
Width = 0.4 meter
Height = 1.5 meter

Since the dimension of bricks is given in centimeter, convert the wall dimension into centimeter

we know that
1 meter = 100 cm

Length = 2.5 m = 250 cm
Width = 0.4 m = 40 cm
Height = 1.5 m = 150 cm

Volume of Wall (V1) = Length x Width x Height

Volume (V1) = 250 x 40 x 150 = 15,00,000 cu cm

Dimension of Brick
Length = 5 cm
Width = 10 cm
Height = 2.5 cm

Volume of Brick (V2) = 5 x 10 x 2.5 = 125 cu cm

No. of bricks used = Volume of wall (V1) /Volume of brick (V2)

Brick Number = 15,00,000/125 = 12,000 bricks

Hence, total of 12,000 bricks are used for making the wall

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