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