Suppose you have a filling in one of your teeth, and, while eating some ice cream, you suddenly realize that the filling came out. One of the reasons the filling may have become detached from your tooth is the differential contraction of the filling relative to the rest of the tooth due to the temperature change. 

(a) Find the change in volume for a metallic dental filling due to the difference between body temperature (37°C) and the temperature of the ice cream you ate (−5°C). The initial volume of the filling is 30 mm³, and its expansion coefficient is α = 42 × 10⁻⁶ K⁻¹. 

(b) Find the change in volume of the cavity. The expansion coefficient of the tooth is α = 17 × 10⁻⁶ K⁻¹.