Answer:[tex]50.831 cm^3[/tex]
Explanation:
Given
Volume of lead ball is [tex]51 cm^3[/tex]
Linear expansion coefficient of lead is [tex]29\times 10^{-6}/^{\circ}C[/tex]
We know [tex]V=V_0\left ( {1+\gamma \left ( \Delta T\right )}\right )[/tex]
Where [tex]V_0[/tex] initial volume
[tex]\gamma [/tex]=Volume expansion coefficient
[tex]\Delta T[/tex]=change in temperature
and [tex]\gamma =3\alpha [/tex]
[tex]V_{70}=V_{40} \left ( 1+\gamma \left ( 78-40\right )\right )[/tex]
[tex]51=V_{40}\left ( 1+87\times 10^{-6}\left ( 38\right )\right )[/tex]
[tex]V_{40}=\frac{51}{1.003306}[/tex]
[tex]V_{40}=50.831 cm^3[/tex]
