At what temperature in C will it fit exactly into a hole of constant diameter 9.997cm?

Question

A steel plug has a diameter of 10000cm at 35 C.the linear expansion coefiecient of steel is 11x10^-6

Answer 1

as you typed the problem - never.
if the correct is that the plug has a 10.000cm dia at 35C, then the difference of the hole and the plug is 0.003 cm and the diameter is going to change 10x11x10^-6 cm/C or 11x10^-5 or 0.00011 cm/C so 0.003/0.00011 or 27.27273 degrees so it will fit at 7.7273C or there abouts.