# A graduated cylinder has a mass of 50 g when empty. When 30 mL of water is added, it has a mass of 120 g. If a rock is added to the graduated cylinder, the level rises to 75 ml and the total mass is now 250 g. What is the density of the rock?

Sep 4, 2017

$\text{density} = 2.9$ ${\text{g/cm}}^{3}$

#### Explanation:

We're asked to find the density of the rock, given some mass and volume information.

We're given that the mass of the system before the rock was added was $120$ $\text{g}$. The mass after the rock was added was $250$ $\text{g}$, so the rock's mass is

color(red)(m_"rock") = m_"final" - m_"initial" = 250color(white)(l)"g" - 120color(white)(l)"g" = color(red)(ul(130color(white)(l)"g"

The initial volume of water in the graduated cylinder was $30$ $\text{mL}$, and the volume after the rock was added read $75$ $\text{mL}$, so the rock's volume is

color(green)(V_"rock") = V_"final" - V_"initial" = 75color(white)(l)"mL" - 30color(white)(l)"mL" = color(green)(ul(45color(white)(l)"mL"

The equation for the density of the rock is

"density" = color(red)("mass")/color(green)("volume")

And so we have

color(blue)("density") = color(red)(130color(white)(l)"g")/color(green)(45color(white)(l)"mL") = color(blue)(ulbar(|stackrel(" ")(" "2.9color(white)(l)"g/mL" = 2.9color(white)(l)"g/cm"^3" ")|)

rounded to $2$ significant figures.