Answer: The percent change in density is (-0.21 %).
Explanation:
Density before raising the temperature:
[tex]\rho_1=\frac{M}{V_1}=\frac{M}{\pi r^2h}[/tex]
Temperature of a metal cylinder is raised from 0.0°C to 110°C.
[tex]h'=h+0.22\%\times h=h+0.0022h=1.0022 h[/tex]
[tex]\rho_2=\frac{M}{V_2}=\frac{M}{\pi r^2h'}=\frac{M}{\pi r^2(1.0022)h}[/tex]
[tex]\text{percentage change}=\frac{rho_2-rho_1}{\rho_1}\times 100[/tex]
[tex]\text{percentage change in density}=\frac{\frac{M}{\pi r^2(1.0022)h}-\frac{M}{\pi r^2h}}{\frac{M}{\pi r^2h}}\times 100=-0.21\%[/tex]
The negative sign indicates that density had been decreased.
The percent change in density is (-0.21 %).
