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?
1 Answer
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
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
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.