`what will the density be if the radius of the sphere is halved, compressing the air within?`

# what will the density be if the radius of the sphere is halved, compressing the air within?

what will the density be if the radius of the sphere is halved, compressing the air within?

### Where am I?

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Given Data

R(say:ρ =1.5 kg/m3ρ =1.5 kg/m3

Taking mass of air inside the sphere as

mFinding the new density (ρ′ρ′) of the air, when the radius of the sphere is made to half i.e.

R/2Initially, the density of the air is expressed as:ρ =m43×π×R3

Now, when the gas is compressed by reducing the radius of sphere to R/2, the density is expressed as:ρ′ =m43×π×(R/2)3

From Equations-1 and 2:ρ′ =8×ρ

ρ′ =8×1.5 kg/m3

ρ′ =12 kg/m3