Respuesta :

Volume of cylinder = pi*r*2*L

As, from the above formula,volume is directly proportional to length, 
So, if we increase in length also increases in volume by 0.22%

we know 

density=mass/volume

As, density is inversely proportional to volume it means increasing in volume decreases the density by 50.22%

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 %).