Question

Density is the ratio of a sample's mass to its volume. A bar of lead has a mass of 115.2 g. When it is submerged in 25.0 mL of water in a graduated cylinder, the water level rises to 35.5 mL. What is the density of the lead

Answer 1

`$10.97 \ g/cm^3$`

Step-by-step explanation:

Given :

Mass of a bar of lead = 115.2 g

Initial water level
`$\text{in the graduated cylinder}$` = 25 mL

Final water level
`$\text{in the graduated cylinder}$` = 35.5 mL

Difference in the water level = 35.5 - 25

= 10.5 mL

=
`10.5 \ cm^3`

We know that when a body is submerged in water, it displaces its own volume of water.

Therefore, the volume of the lead bar = volume of the water displaced = 10.5 mL =
`10.5 \ cm^3`

We know that mathematically, density is the ratio of mass of body to its volume.

Density of the lead bar is given by :

`$\rho =\frac{\text{mass}}{\text{volume}}$`

`$\rho =\frac{\text{115.2 g}}{\text{10.5 cm}^3}$`

=
`$10.97 \ g/cm^3$`