Question

When the temperature of a metal cylinder is raised from 0.0°C to 110°C, its length increases by 0.22%. Find the percent change in density.

Answer 1

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 2

Answer: The percent change in density is (-0.21 %).

Step-by-step explanation:

Density before raising the temperature:

`\rho_1=(M)/(V_1)=(M)/(\pi r^2h)`

Temperature of a metal cylinder is raised from 0.0°C to 110°C.

`h'=h+0.22\%* h=h+0.0022h=1.0022 h`

`\rho_2=(M)/(V_2)=(M)/(\pi r^2h')=(M)/(\pi r^2(1.0022)h)`

`\text{percentage change}=(rho_2-rho_1)/(\rho_1)* 100`

`\text{percentage change in density}=((M)/(\pi r^2(1.0022)h)-(M)/(\pi r^2h))/((M)/(\pi r^2h))* 100=-0.21\%`

The negative sign indicates that density had been decreased.

The percent change in density is (-0.21 %).