A circular steel plate of radius 15 cm is cooled from 350oC to 20oC.?

Question

By what percentage does the plate’s area decrease?

Answer 1

We know that
A=piR^2
% change = [(A2-A1)/A1]x100%
Linear expansion is a change in a dimension ((Radius in in our case) is a product of change in temperature t , coefficient of liner expansion k and original radius (R1 in this case)

R2-R1= R1 k (t2-t1)
R2= R1 k (t2-t1) + R1=
R2=R1(k (t2-t1)+1)

A1= piR1^2
A2= pi[R1(k (t2-t1)+1)]^2

A2-A1= piR1^2[(k (t2-t1)+1)^2 -1]

%= [piR1^2[(k (t2-t1)+1)^2 -1]/piR1^2]x 100%
%= [(k (t2-t1)+1)^2 -1]x 100%

since k for Stainless steel 17.3 E-6/K
and k for Iron or Steel 11.1 E-6 /K

lets take it k=12
%=[12E-6(20 - 350)+ 1 ]^2 - 1]x100%
%=0.79%