Density GCSE physics lesson: ρ = m ÷ V, floating and sinking, and the required practical

Density: the required practical

Each question gives made-up results from the density practical. Work out the volume first, then the density, in g/cm³. Show your working on paper.

1. A rectangular block measures 4.0 cm by 3.0 cm by 2.5 cm. What is its volume, in cm³?
2. On a balance, the same block has a mass of 81 g. What is its density, in g/cm³?
3. A stone is lowered on a thread into a full eureka can. 35 cm³ of water runs into the measuring cylinder. The stone's mass is 91 g. What is its density, in g/cm³?
4. Why is the eureka can filled until water runs out of its spout, and left until it stops, before the stone goes in?
   1. So that all the water the stone pushes aside comes out of the spout
   2. So that there is enough water for the stone to float in
   3. So that the water is the same temperature as the stone
5. A measuring cylinder holds water up to 60 cm³. A brass key of mass 119 g is lowered in, and the level rises to 74 cm³. What is the key's density, in g/cm³?
6. An empty measuring cylinder on a balance reads 96 g. With 50 cm³ of oil poured in, it reads 142 g. What is the oil's density, in g/cm³?
7. How should you read the volume of water in a measuring cylinder?
   1. From above, at the top of the curved surface
   2. With your eye level with the bottom of the curved surface (the meniscus)
   3. Where the water touches the glass at the side

Density: practice

Show your working on paper. Write the mass and the volume with their units first. 1 g/cm³ = 1000 kg/m³. The stretch is optional.

Diagnostic question: choose and explain

1. A stone of mass 300 g pushes 120 cm³ of water out of a eureka can. What is its density in kg/m³?
   1. 2.5 kg/m³
   2. 400 kg/m³
   3. 2500 kg/m³
   4. 0.0025 kg/m³

Practice questions

1. A block of wood has a mass of 600 g and a volume of 750 cm³. What is its density, in g/cm³?
2. A plastic box has a mass of 2.0 kg and a volume of 0.0025 m³. What is its density, in kg/m³?
3. Change the units: 0.92 g/cm³ = ___ kg/m³, and 7800 kg/m³ = ___ g/cm³.
4. 1 g of water is about 1 cm³. As steam it takes up about 1700 cm³. Why?
   1. The particles in steam are much smaller
   2. The particles in steam weigh less
   3. The same particles are much further apart, so the same mass takes up far more space
   4. Steam has fewer particles in each gram
5. Concrete has a density of 2400 kg/m³. What is the mass, in kg, of a concrete block with a volume of 0.20 m³?
6. Olive oil has a density of 0.92 g/cm³. What volume, in cm³, does 184 g of it take up?
7. A plastic toy has a density of 0.95 g/cm³. It is put in oil (0.92 g/cm³), then in water (1.0 g/cm³). What happens?
   1. It floats in both
   2. It sinks in both
   3. It floats in water and sinks in oil
   4. It floats in oil and sinks in water
8. Kai measures a pebble's volume by the rise of the water in a measuring cylinder. Air bubbles cling to the pebble. What does this do to the density he works out?
   1. It comes out too big
   2. It comes out too small
   3. It makes no difference
9. A metal block measures 2.0 cm by 3.0 cm by 5.0 cm and has a mass of 0.267 kg. What is its density in kg/m³?
10. An empty measuring cylinder has a mass of 85 g. With 60 cm³ of a liquid in it, its mass is 160.6 g. What is the liquid's density, in g/cm³?
11. Stretch: a sealed, hollow steel ball has a mass of 600 g and takes up 750 cm³. Its average density is ___ g/cm³, so in water it ___. Solid steel (7.8 g/cm³) the same size would have a mass of ___ g.

Support: Write m = and V = with their units before anything else. Work in g/cm³ first; to change to kg/m³, multiply by 1000, and check the kg/m³ number is the bigger one.

Density: exit

Write the mass and the volume with their units first.

1. A pebble of mass 52 g is lowered into a measuring cylinder, and the water rises from 30 cm³ to 50 cm³. What is its density, in g/cm³?
2. What is the pebble's density in kg/m³?

Exit check

A pebble in a measuring cylinder shows who takes the rise in the level and who can change the units.

A pebble of mass 52 g is lowered into a measuring cylinder: the water rises from 30 cm³ to 50 cm³.

Density

Write the mass and the volume with their units before each calculation. 1 g/cm³ = 1000 kg/m³. Show your working.