An iron sphere has a radius `8 cm` at a temperature of `0^(@)C`. Calculate the change in volume of the sphere if is temperature is raised to `80^(@)C`. Coefficient of liner expansion of iron `=11xx10^(-6) .^(@)C^(-1)`.

Answer

`[5.66cm^(3)]`

Explanation

Here, `R=8` cm, Volume of sphere at `0^(@)C` is
`V_(0)=(4)/(3)pi R_(3)=(4)/(3)xx(22)/(7)xx8^(3)cm^(3)`
Increase in temperature, `DeltaT=80-0-80 .^(@)C`
Coefficient of cubical expansion of iron `gamma=3 alpha=3xx11xx10^(-6) .^(@)C^(-1)`
Change in volume, `Delta V=V_(0) gamma Delta T`
`=((4)/(3)xx(22)/(7)xx8^(3))xx(3xx11xx10^(-6)xx80=5.66cm^(3)`