A square shape hole, 8.79cm along each side, is cut in a sheet of metal. If the

Question

A square shape hole, 8.79cm along each side, is cut in a sheet of metal. If the temperature of the sheet is increased by 62.9K, the area of the hole increases by 0.158 cm2. Find the coefficient of linear expansion of the metal.

Answer in /C and in 3 SF. (Example: 3.21E-3)

Quick arithmetic gives me an answer of 6.08E-6, but I'm not sure if that's linear expansion, or area expansion. Our textbook doesn't even mention area expansion.

I got that number by solving for in this equation:

A = . A . T

A = 77.3 cm
T = 62.9 K = 336.05 C
A = 0.158 cm2

Also, do I have to convert cm to m or it doesn't make a difference? Thanks a lot.

Explanation / Answer

Acc. to area expansion formula we have , = A / A (T) Given data :    initial area ,A = 77.3 cm2 the change in temparature is the change in any scale here , you convert in to ceslius scale , it is a mistake so, we have to consider , the change of temaprature is as , T = 62.9 K or oC change of area due to expansion ,A = 0.158 cm2 thus, expansion co-efficent ,     = (0.158 cm2 ) / (77.3 cm2 )(62.9 oC)        = 3.249 x10-5 / oC

the change in temparature is the change in any scale here , you convert in to ceslius scale , it is a mistake so, we have to consider , the change of temaprature is as , T = 62.9 K or oC change of area due to expansion ,A = 0.158 cm2 thus, expansion co-efficent ,     = (0.158 cm2 ) / (77.3 cm2 )(62.9 oC)        = 3.249 x10-5 / oC

thus, expansion co-efficent ,     = (0.158 cm2 ) / (77.3 cm2 )(62.9 oC)        = 3.249 x10-5 / oC

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