A solid sphere of copper weighs 1 kg, Find the increase in its surface area when its temperature rises from 15^(0)C to 500^(0)C. Relative density of copper at 0^(0)C is 8.93. alpha=16.07xx10^(-6)//""^(0)C

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

1.	A solid sphere of copper weighs 1 kg, Find the increase in its surface area when its temperature rises from 15^(0)C to 500^(0)C. Relative density of copper at 0^(0)C is 8.93. alpha=16.07xx10^(-6)//""^(0)C
Answer» Solution :`r_(0)=[(1000)/(4//3pi)]^(1//3)=2.99cm, r_(15)" at " 15^(0)C` `r_(15)=r_(0) (1+alpha Delta THETA)=2.99(1+16.07xx10^(-6)xx15)=2.991cm therefore " AREA at " 15^(0)C=A_(15)=4PI r_(15)^(2)=112.4cm^(2)`. At `500^(0)` the radius is `r_(500)=2.99(1+alpha xx 500)=3.014` `A_(500)=4pi r_(500)^(2)=114.2 cm^(2)` Hence increase in surface area `DeltaA=A_(500)-A_(15)=114.2-112.4=1.8cm^(2)`