Question

1.4 The inside of a sports hall measures 80 m

long by 40 m wide by 15 m high. The air in
it has a density of 1.3 kg/m when it is cool.

a Calculate the volume of the air in the
sports hall,

b Calculate the mass of the air. State the
equation you are using.​

Answer 1

a)
`48000 m^3`

The volume of the sports hall can be calculated using the equation

`V=a\cdot b \cdot c`

where

a, b, c are the measures of the sizes of the hall

For the sport hall in this problem, we have

a = 80 m

b = 40 m

c = 15 m

Substituting into the equation, we find

`V=(80)(40)(15)=48,000 m^3`

b)
`62400 kg`

Being a gas, the air fills the whole sport halls, therefore its volume is equal to the volume of the sports hall.

The relationship between the mass, the volume and the density of the air is

`\rho = (m)/(V)`

where

`\rho` is the density

m is the mass

V is the volume

Here we have:

`\rho = 1.3 kg/m^3`

`V=48000 m^3`

Solving for m, we find the mass of air:

`m=\rho V = (1.3)(48000)=62,400 kg`