The Coefficient of Linear Expansion of Copper Is $17 \times 10 ^ { - 6 } K^{ - 1}$

The coefficient of linear expansion of copper is $17 \times 10 ^ { - 6 } K^{ - 1}$ and that of steel is $12 \times 10 ^ { - 6 } K^{ - 1}$ At $12 ^ { \circ } \mathrm { C }$ a steel rod has a diameter of 2.540 cm and a copper pipe has a diameter of 2.536 cm. Which one of the following quantities is closest to the temperature to which the copper pipe must be heated in order for the unheated steel rod to fit snugly in the copper pipe?

A) $143 ^ { \circ } \mathrm { C }$
B) $93 ^ { \circ } \mathrm { C }$
C) $53 ^ { \circ } \mathrm { C }$
D) $105 ^ { \circ } \mathrm { C }$
E) $81 ^ { \circ } \mathrm { C }$