Question

The dimension of my Hall are 10m×7m×5m. If the density of the air is 1.11gm³find the mass of the air in the Hall

Answer 1

Question :-

The dimension of a hall is 10m x 7m x 5m . If the density of the air is 1.11 g/m³ . Find the mass of the air in the Hall ?

Answer :-

Given :-

The dimension of the hall is 10m x 7m x 5m .

Density of the air is 1.11 g/m³.

Required to find :-

Mass of the air in the Hall ?

Formulae used :-

$\large{\leadsto{\boxed{\rm{Volume\;of\;a\; cuboid = Length \times Breadth \times height }}}}$

$\large{\leadsto{\boxed{\rm{ Mass = Density \times Volume }}}}$

Solution :-

Given that :-

The dimension of the hall is 10m x 7m x 5m .

So,

• Length of the hall = 10 meters

• Breadth of the hall = 7 meters

• Height of the hall = 5 meters

Hence,

Using the formula ,

$\large{\leadsto{\boxed{\rm{Volume\;of\;a\; cuboid = Length \times Breadth \times height }}}}$

So,

Volume of the hall = 10 meters x 7 meters x 5 meters

Volume of the hall = 350 m³

Here,

The volume of the hall = Volume of the air in the hall

This is because,

We know that,

Air is a gas which has very less intermolecular spaces so it can flow anywhere.

It is concluded that the Hall is full of air .

So,

Volume of the air is 350 m³ .

Similarly,

It is also given that,

Density of the air = 1.11 g/m³

Using the formula,

$\large{\leadsto{\boxed{\rm{ Mass = Density \times Volume }}}}$

So,

$\longrightarrow{\mathsf{Mass = 1.11 g/m^3 \times 350 m^3 }}$

Here m³ gets cancelled

$\longrightarrow{\mathsf{Mass = 1.11 g \times 350 }}$

$\red{\implies{\underline{\tt{ Mass = 388.5\; grams }}}}$

$\large{\leadsto{\boxed{\tt{\therefore{Mass \; of \; air = 388.5\; grams }}}}}$

Points to remember :-

Density is the ratio of mass is to volume .

This is represented as,

$\tt{Density = \dfrac{Mass}{Volume}}$

This formula can be modified when we want to find any physical quantity when any two of them are given .

Remember,

Since hall is in the shape of a cuboid we used the formula ,

Volume = length x breadth x height

The formula depending on the measurement or name of the figure mentioned.

Answer 2

Answer:

Question :-

The dimension of a hall is 10m x 7m x 5m . If the density of the air is 1.11 g/m³ . Find the mass of the air in the Hall ?

Answer :-

Given :-

The dimension of the hall is 10m x 7m x 5m .

Density of the air is 1.11 g/m³.

Required to find :-

Mass of the air in the Hall ?

Formulae used :-

\large{\leadsto{\boxed{\rm{Volume\;of\;a\; cuboid = Length \times Breadth \times height }}}}⇝

Volumeofacuboid=Length×Breadth×height

\large{\leadsto{\boxed{\rm{ Mass = Density \times Volume }}}}⇝

Mass=Density×Volume

Solution :-

Given that :-

The dimension of the hall is 10m x 7m x 5m .

So,

Length of the hall = 10 meters

Breadth of the hall = 7 meters

Height of the hall = 5 meters

Hence,

Using the formula ,

\large{\leadsto{\boxed{\rm{Volume\;of\;a\; cuboid = Length \times Breadth \times height }}}}⇝

Volumeofacuboid=Length×Breadth×height

So,

Volume of the hall = 10 meters x 7 meters x 5 meters

Volume of the hall = 350 m³

Here,

The volume of the hall = Volume of the air in the hall

This is because,

We know that,

Air is a gas which has very less intermolecular spaces so it can flow anywhere.

It is concluded that the Hall is full of air .

So,

Volume of the air is 350 m³ .

Similarly,

It is also given that,

Density of the air = 1.11 g/m³

Using the formula,

\large{\leadsto{\boxed{\rm{ Mass = Density \times Volume }}}}⇝

Mass=Density×Volume

So,

\longrightarrow{\mathsf{Mass = 1.11 g/m^3 \times 350 m^3 }}⟶Mass=1.11g/m

3

×350m

3

Here m³ gets cancelled

\longrightarrow{\mathsf{Mass = 1.11 g \times 350 }}⟶Mass=1.11g×350

\red{\implies{\underline{\tt{ Mass = 388.5\; grams }}}}⟹

Mass=388.5grams

\large{\leadsto{\boxed{\tt{\therefore{Mass \; of \; air = 388.5\; grams }}}}}⇝

∴Massofair=388.5grams

Points to remember :-

Density is the ratio of mass is to volume .

This is represented as,

\tt{Density = \dfrac{Mass}{Volume}}Density=

Volume

Mass

This formula can be modified when we want to find any physical quantity when any two of them are given .

Remember,

Since hall is in the shape of a cuboid we used the formula ,

Volume = length x breadth x height

The formula depending on the measurement or name of the figure mentioned.