When the temperature of a “copper” penny (which is not really copper) is raised

Question

When the temperature of a “copper” penny (which is not really copper) is raised by 100 C, its diameter increases by 0.18%.
a). What is the coefficient of linear expansion?
b).What is the percent increase in the thickness of the penny?
c). What is the percent increase in the face (flat surface, not the actual face of Lincoln!) of the penny?
d). What is the percent increase in the volume of the penny?
e). What is the percent increase in the mass of the penny?

I tried working it out but my units wouldn't cancel then I ended up with a weird equation leftover.

Explanation / Answer

let initial diameter be 100 ;

new diameter = 100.18 ;

A / A = ( 0.18 / 100 ) ^2 = 3.24 e -6

3.24 e - 6 = A . T ;

or A =( 3.24 e - 6 ) / ( 100 ) = 3.24 e - 8 ;

A = ( 2 / 3 ) V ;

or  3.24 e - 8 =  ( 2 / 3 ) V ;

or V = 4. 86 e - 8 ;

V = 3 L or L = 1.62 e -8 ;

( a ) L = 1.62 e -8 ;

( b ) % inc in thickness of penny = L . T = 1.62 e -8 * 100 * 100 = 1.62 e - 4 ;

( c ) % inc in face = A . T * 100 = ( 3.24 e - 8 ) * 100 * 100 = 3.24 e -4 ;

( d ) % inc in volume = V . T *100 = 4. 86 e - 8 * 100 * 100 = 4.86 e -4 ;

( e ) mass doesnt dchange , so answer is 0

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