# Density – problems and solutions

1. The volume of an object is 8 cm^{3} and mass of an object is 84 gram. What is the density of the object?

__Known :__

Volume (V) = 8 cm^{3}

Mass (m) = 84 gram

__Wanted :__ density (ρ)

__Solution :__

ρ = m / V = 84 gram / 8 cm^{3 }= 10.5 gram/cm^{3}

2. Volume of an block is 5 cm^{3}. If the density of the block is 250 g/cm^{3}, what is the mass of the block ?

__Known :__

Volume (V) = 5 cm^{3}

Density (ρ) = 250 g/cm^{3}

__Wanted :__ Mass of the block

__Solution :__

ρ = m / V

*ρ = density, V = volume, m = mass*

Mass of block :

m = ρ V = (250 g/cm^{3})(5 cm^{3}) = 1250 gram

3. Volume of water is 35 cm^{3} and mass of water is 60 gram, what is the density of the water.

__Known :__

Volume of water (V) = 35 cm^{3}

Mass of water (m) = 60 gram

__Wanted:__ density (ρ)

__Solution :__

density :

ρ = m / V = 60/35 = 1.71 gram/cm^{3}

4. Mass of an metal is 120 gram and volume of an metal is 60 cm

^{3}. What is the density of the metal?

__Known :__

Mass (m) = 120 gram

Volume (V) = 60 cm^{3}

__Wanted :__ density

__Solution :__

ρ = m / V

ρ = 120 gram / 60 cm^{3}

ρ = 2 gram/cm^{3}

5.

Based on the table, an object with the same density is…

Solution :

Formula of density :

ρ = m / V

ρ = density, m = mass, V = volume

6. Based on the figure below, if the mass of an object is 300 gram, what is the density of the object.

__Known :__

Mass (m) = 300 gram

Volume (V) = volume of spilled water = 20 cm^{3}

__Wanted :__ density

__Solution :__

ρ = m / V = 300 gram / 20 cm^{3 }= 15 gram/cm^{3 }

7. Mass of object is 316 gram, placed in a container as shown in figure. What is the density of the object.

__Known :__

Mass (m) = 316 gram

Volume (V) = volume of spilled water = 40 ml

__Wanted :__ density

__Solution :__

Mass = 316 gram = 316/1000 kg = 0.316 kg

Volume = 40 ml = 40/1000 liters = 4/100 liters = 0.04 liters

1 liter = 1 dm^{3} = 1/1000 m^{3 }= 0.001 m^{3}

0.04 liters = (0.04)(0.001) m^{3} = 0.00004 m^{3}

Density :

ρ = m / V = 0.316 kg / 0.00004 m^{3 }= 316 kg / 0.04 m^{3} = 7900 kg/m^{3 }

8.

The density of stone based on the image is…

__Known :__

Mass (m) = 100 gram + 20 gram = 120 gram = 120 / 1000 kilogram = 0.120 kilogram

Volume (V) = 80 ml – 60 ml = 20 ml = 20 / 1000 liters = 2/100 liters = 0.02 liters

1 liter = 1 dm^{3 }= 1/1000 m^{3 }= 0.001 m^{3}

0.02 liters = 0.02 x 0.001 m^{3} = 0.00002 m^{3}

__Wanted :__ density

__Solution :__

Density :

ρ = m / V = 0.120 kg / 0.00002 m^{3 }= 120 kg / 0.02 m^{3} = 6000 kg/m^{3}