A solid sphere of copper weighs 1kg, Find the increase in its surface area when its temperature rises from 15^(@)C" to "500^(@)C. Relative density of copper at 0^(@)C is 8.39. alpha=16.07xx10^(-6)//""^(0)C

A solid sphere of copper weighs 1kg, Find the increase in its surface

1.	A solid sphere of copper weighs 1kg, Find the increase in its surface area when its temperature rises from 15^(@)C" to "500^(@)C. Relative density of copper at 0^(@)C is 8.39. alpha=16.07xx10^(-6)//""^(0)C
Answer» Solution :`r_(0) = [ (1000)/(4//3 pi) ]^(1//3)= 2.99 cm , r_(15) " at " 15^(0)C` `r_(15) = r_(0) ( 1 + alpha Delta THETA) = 2.99 (1 + 16.07 xx 10^(-6) xx 15) =2.99 1` cm `therefore ` Area at `15^(@)C = A_(15) = 4 pi r_(15)^(2) = 112.4cm^(2)` At `500^(0)` the radius is `r_(500)` = 2.99 `(1 + alpha xx 500)` = 3.014 `A_(500) = 4 pi r_(500)^(2) = 114.2cm^(2)` HENCE increase in surf ace area `Delta A = A_(500) - A_(15)114.2 - 112.4 = 1.8cm^(2)`