Question

A metal rod, when placed in a very hot oven, is observed to expand by about 0.1%. By approximately what fraction does the surface area of a sheet made of the same metal increase when placed in the same oven?

Answer 1

$\Delta L=\alpha L_0\Delta T$

$\frac {\Delta L}{L_0}=\alpha \Delta T$

$0.1=\alpha \Delta T$

$\frac {\Delta A}{A_0}=2\alpha \Delta T$

$\frac {\Delta A}{A_0}=2\cdot 0.1=0.2$

0.2% increase in the area of the sheet.