Answer
(a) The change in volume of the metallic dental filling is $-0.053~mm^3$
(b) The change in volume of the cavity is $-0.021~mm^3$
Work Step by Step
(a) We can find the change in volume due to the decrease in temperature:
$\Delta V = \beta~\Delta T~V$
$\Delta V = (42\times 10^{-6}~K^{-1})(-42~K)(30~mm^3)$
$\Delta V = -0.053~mm^3$
The change in volume of the metallic dental filling is $-0.053~mm^3$
(b) We can find the change in volume due to the decrease in temperature:
$\Delta V = \beta~\Delta T~V$
$\Delta V = (17\times 10^{-6}~K^{-1})(-42~K)(30~mm^3)$
$\Delta V = -0.021~mm^3$
The change in volume of the cavity is $-0.021~mm^3$
