**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**