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
Nathan L.
Sep 4, 2017

#"density" = 2.9# #"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# #"g"#. The mass after the rock was added was #250# #"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# #"mL"#, and the volume after the rock was added read #75# #"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.

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