A small cube of metal measures 19.4 mm on a side and weighs 80.1 g. What is the density of the metal in g/cm^3?

1 Answer
Sep 5, 2016

Answer:

The density of the metal is #"11.0 g/cm"^3#.

Explanation:

The density(#ρ#) of anything is its mass (#m#) divided by its volume (#V#).

#color(blue)(|bar(ul(color(white)(a/a) ρ = m/Vcolor(white)(a/a)|)))" "#

The volume of a cube is

#color(blue)(|bar(ul(color(white)(a/a) V = l^3color(white)(a/a)|)))" "#

where #l# is the length of an edge.

#V = l^3 = ("19.4 mm")^3 = "7301 mm"^3#

We must convert cubic millimetres to cubic centimetres.

#V = 7301 color(red)(cancel(color(black)("mm"^3))) × ("1 cm"/(10color(red)(cancel(color(black)("mm")))))^3 = "7.301 cm"^3#

#ρ = m/V = "80.1 g"/("7.301 cm"^3) = "11.0 g/cm"^3#