## Question

A cylinder of diameter exactly 1 cm at 30^{o}C is to be inserted into a hole in a steel plate. The hole has a diameter of 0.99967 cm at 30^{o}C. If α for steel is ^{o}C^{-1}, to what temperature must the plate be heated?

### Solution

60^{o}C

The hole will expand in the same way as a circle of steel filling it would expands. The diameter of the hole needs to be increased by

Now,

Therefore, the plane must be raised to a temperature of 30 + 30 = **60 ^{o}C**

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