Measure a density — questions

1. calculate

A metal block measures 5.0 cm by 4.0 cm by 2.0 cm and has a mass of 108 g. Calculate (a) its volume and (b) its density, to 2 significant figures.

(a) Volume of the block: ______________ unit ________

(b) Density of the metal: ______________ unit ________

Nudge (only if you are stuck): Volume of a block = length × width × height. Then density = mass ÷ volume.

2. describe

Put the steps for finding the density of a small, irregular stone in order. The steps are listed in a mixed order.

Write the number of each step in order.

1. Read the new level
2. Weigh the dry stone on a balance
3. Divide the mass by the volume
4. Lower the stone on a thread until it is completely under water
5. Pour water into a measuring cylinder and read the level
6. Subtract the first reading from the second to find the volume

• Step 1: ______
• Step 2: ______
• Step 3: ______
• Step 4: ______
• Step 5: ______
• Step 6: ______

Nudge (only if you are stuck): Weigh the stone while it is still dry. What do you need to read before the stone goes into the water?

3. calculate

A dry stone has a mass of 30.0 g. A measuring cylinder contains water up to 35 cm³. When the stone is completely under water, the level is 47 cm³. Calculate (a) the volume of the stone and (b) its density, to 2 significant figures.

(a) Volume of the stone: ______________ unit ________

(b) Density of the stone: ______________ unit ________

Nudge (only if you are stuck): Which part of the 47 cm³ is the stone?

4. calculate

An empty measuring cylinder on a balance reads 92.0 g. A pupil pours in 40 cm³ of syrup and the balance then reads 148.4 g. (a) Calculate the mass of the syrup. (b) Calculate the density of the syrup, to 2 significant figures.

(a) Mass of the syrup: ______________ unit ________

(b) Density of the syrup: ______________ unit ________

Nudge (only if you are stuck): The balance is weighing two things. How do you take the cylinder away?

5. calculate

An ice cube has a volume of 27.0 cm³. The density of ice is 0.92 g/cm³. Calculate the mass of the ice cube, to 2 significant figures.

Mass of the ice cube: ______________ unit ________

Nudge (only if you are stuck): Rearrange ρ = m / V to make m the subject.

6. calculate

Cooking oil has a density of 0.92 g/cm³. What is its density in kg/m³?

Density of the oil: ______________ unit ________

Nudge (only if you are stuck): 1 g/cm³ = 1000 kg/m³. Is a density in kg/m³ a bigger or a smaller number?

7. identify / explain

A pupil finds the density of a stone by displacement. In each case below only the one thing named goes wrong; every other measurement is made correctly. Which of these would make the measured density too small?

Tick every correct statement.

• An air bubble stays stuck to the stone under water
• The pupil uses the new level as the stone’s volume
• The stone is weighed while it is still wet (its volume is measured correctly)
• The levels are read at the bottom of the meniscus
• Some water splashes out as the stone goes in

Why do your choices make the density too small?

Nudge (only if you are stuck): Density = mass ÷ volume. A density comes out too small if the mass is too small or the volume too big.

8. calculate / explain

A rock is too big to fit into any measuring cylinder. Its mass is 230 g. It is lowered into a displacement can filled with water to the spout, and the water that runs out of the spout is collected: 85 cm³. (a) Calculate the density of the rock, to 2 significant figures. (b) Explain why the water collected has the same volume as the rock.

(a) Density of the rock: ______________ unit ________

(b) Why does the collected water have the same volume as the rock?

Nudge (only if you are stuck): The can was full to the spout. Where does the water pushed aside by the rock go?

9. calculate / suggest

A ring looks like gold. Its mass is 9.7 g. Lowered into a narrow measuring cylinder marked every 0.1 cm³, it raises the level from 5.0 cm³ to 5.5 cm³. Gold has a density of 19.3 g/cm³ and brass 8.5 g/cm³. (a) Calculate the density of the ring, to 2 significant figures. (b) Is the ring more likely gold or brass? (c) Suggest why the cylinder has to be narrow.

(a) Density of the ring: ______________ unit ________

(b) Gold or brass? (c) Why a narrow cylinder?

Nudge (only if you are stuck): Find the volume as a rise, then divide. Which listed density is your answer close to?