Required Practical: Measuring Density

This lesson covers the AQA Required Practical for determining the density of regular and irregular solids and liquids (AQA 8464, Required Practical 15). You must understand the methods, equipment, calculations and sources of error involved.

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Measuring the Density of a Regular Solid

A regular solid has a simple geometric shape (cuboid, cylinder or sphere) whose volume can be calculated from measured dimensions.

Method

1. Measure the mass of the object using an electronic balance (in grams).
2. Measure the dimensions using a ruler, vernier calliper or micrometer:
   • Cuboid: measure length ($l$l), width ($w$w) and height ($h$h)
   • Cylinder: measure diameter (then calculate radius $r$r) and height ($h$h)
3. Calculate the volume:
   • Cuboid: $V = l \times w \times h$V=l×w×h
   • Cylinder: $V = \pi r^2 h$V=πr2h
4. Calculate density: $\rho = m / V$ρ=m/V.

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Measuring the Density of an Irregular Solid

An irregular solid (e.g. a stone or a key) does not have a simple shape, so you cannot calculate its volume from dimensions. Instead, use the displacement method.

Method 1: Measuring Cylinder

1. Measure the mass of the object using an electronic balance.
2. Fill a measuring cylinder with water and record the initial volume $V_1$V1​.
3. Carefully lower the object into the water (it must be fully submerged).
4. Record the new volume $V_2$V2​.
5. Volume of object = $V_2 - V_1$V2​−V1​.
6. Calculate density: $\rho = m / V$ρ=m/V.

Method 2: Eureka Can (Displacement Can)

1. Measure the mass of the object.
2. Fill the eureka can until water just reaches the spout.
3. Place a measuring cylinder under the spout.
4. Carefully lower the object into the can.
5. Collect the displaced water in the measuring cylinder — this volume equals the volume of the object.
6. Calculate density: $\rho = m / V$ρ=m/V.

graph LR
    A["Measure mass<br/>on balance"] --> B["Lower object into<br/>eureka can"]
    B --> C["Displaced water<br/>collected in cylinder"]
    C --> D["Read volume<br/>of displaced water"]
    D --> E["Calculate ρ = m / V"]

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Measuring the Density of a Liquid

Method

1. Place an empty measuring cylinder on the balance and record its mass $m_1$m1​.
2. Pour the liquid into the measuring cylinder and record the volume $V$V.
3. Record the total mass (cylinder + liquid) $m_2$m2​.
4. Mass of liquid = $m_2 - m_1$m2​−m1​.
5. Calculate density: $\rho = m / V$ρ=m/V.

Exam Tip: Always subtract the mass of the container. A common error is to use the total mass (container + liquid) in the calculation, giving an incorrectly high density.

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Reading the Meniscus

When reading a measuring cylinder:

• Place the cylinder on a flat surface.
• Read at eye level.
• Read the bottom of the meniscus (the curved surface of the liquid).

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Sources of Error and Improvements

Source of Error	Improvement
Air bubbles trapped on the surface of an irregular solid	Gently tap the object or tilt the cylinder to release bubbles
Water left on the surface of the object before measuring mass	Dry the object thoroughly before measuring mass
Parallax error when reading the measuring cylinder	Read at eye level at the bottom of the meniscus
Measuring dimensions inaccurately for regular solids	Use vernier callipers or a micrometer for more precise measurements
Measuring cylinder too large for small volumes	Use a smaller measuring cylinder with finer graduations
Water splashing when the object is dropped in	Lower the object gently using a thread or string

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Worked Example

A student measures the density of a stone. The stone has a mass of 65 g. She places it in a measuring cylinder containing 40 cm³ of water. The water level rises to 65 cm³. Calculate the density of the stone.

$V = V_2 - V_1 = 65 - 40 = 25 \text{ cm³}$V=V2​−V1​=65−40=25 cm³

$\rho = \frac{m}{V} = \frac{65}{25} = 2.6 \text{ g/cm³}$ρ=Vm​=2565​=2.6 g/cm³

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Comparing Methods

Method	Suitable for	Advantage	Limitation
Ruler + calculation	Regular solids	Simple and quick	Only works for simple shapes
Measuring cylinder (displacement)	Small irregular solids	Accurate for small objects	Object must fit inside and be denser than water
Eureka can	Larger irregular solids	Works for objects too large for a measuring cylinder	Requires careful setup; water must be at the spout level before adding the object

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Common Misconceptions

Misconception	Correction
You can measure the volume of any object by calculating from its dimensions	Only for regular shapes — irregular solids require the displacement method
The mass changes when you put an object in water	Mass does not change — always measure mass before putting the object in water or dry it first
It doesn't matter where you read the measuring cylinder	You must read at eye level at the bottom of the meniscus to avoid parallax error

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Summary

• For regular solids: measure mass with a balance and calculate volume from dimensions, then use $\rho = m / V$ρ=m/V.
• For irregular solids: use the displacement method (measuring cylinder or eureka can) to find volume.
• For liquids: measure the mass of the liquid in a measuring cylinder (subtract the mass of the empty cylinder).
• Key sources of error include parallax errors, trapped air bubbles and water on the object's surface.
• This is an AQA Required Practical — you must know the method, equipment and sources of error.

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Equipment List (Know This For the Exam)