PhysicsICSE Class 8 · Physical Quantities and Measurement

Measuring Density with a Eureka Can and Cylinder, and Floating and Sinking (ICSE Class 8)

Q: How do you find the volume of an irregular solid?

Lower it into water in a measuring cylinder and subtract the initial reading from the final reading; for a large solid use a eureka can and measure the overflow.

Q: Why do some objects float and others sink?

An object floats if its density is less than that of the liquid and sinks if its density is more.

Q: How does a steel ship float?

The hollow ship contains air, so its average density (steel plus air) is less than the density of water.

Updated 17 October 2026 · Fact-checked

The volume of an irregular solid is found by displacement of water, either as the rise in level in a measuring cylinder (V₂ − V₁) or as the water overflowing from a eureka can; its density is then m/V. An object floats if it is less dense than the liquid and sinks if it is denser.

The water level rise V₂ − V₁ is the solid's volume, and density is m/V; objects less dense than water float, denser ones sink.

Illustration drawn for QuestionBuddy.

Understand Measuring the Density of Solids and Liquids; Floating and Sinking

Irregular solid and a measuring cylinder.
1. Pour water into the cylinder and read the level $V_{1}$ (bottom of the meniscus, eye level).
2. Tie the solid to a thread and lower it gently until fully under water. Read $V_{2}$ .
3. Volume $= V_{2} - V_{1}$ (in mL = cm³).
4. Find the mass with a balance; then $ρ = \frac{m}{V}$ .
The solid must sink and must not dissolve in or absorb water.

Eureka (overflow) can. For a solid too large for the cylinder:
1. Fill the can until water flows out of the spout; wait until dripping stops.
2. Place an empty measuring cylinder under the spout.
3. Lower the solid on a thread into the can.
4. The volume of water collected equals the volume of the solid.

Density of a liquid.
1. Find the mass $m_{1}$ of an empty beaker.
2. Pour in a measured volume $V$ using a measuring cylinder; find the new mass $m_{2}$ .
3. $ρ = \frac{m _{2} - m _{1}}{V}$ .
A density bottle holding a fixed volume can also be used.

Floating and sinking.

Object less dense than the liquid: it floats.
Object denser than the liquid: it sinks.
Equal densities: it stays where it is placed in the liquid.

Examples in water (1 g/cm³): wood and ice float; iron and stone sink. A less dense liquid floats on a denser one (oil on water). A hollow steel ship floats because its average density (steel plus the air inside) is less than that of water.

Ice. Ice (about 0.92 g/cm³) is less dense than water, so ice floats and ponds freeze from the top.

Draw-and-label checklist (eureka can): can with spout, water at spout level, solid on thread, measuring cylinder under spout.

Measuring the Density of Solids and Liquids; Floating and Sinking: formulas and key facts

Volume by displacement: $V = V_{2} - V_{1}$; Cylinder readings (mL = cm³).
Density of a liquid: $ρ = \frac{m _{2} - m _{1}}{V}$; m₁ empty beaker, m₂ with liquid.
Floating and sinking: Less dense than liquid floats
Denser than liquid sinks
Equal stays inside; Compare densities.

Less dense than liquid	floats
Denser than liquid	sinks
Equal	stays inside

How to solve Measuring the Density of Solids and Liquids; Floating and Sinking questions

First find the volume, then the density, then compare with the liquid.

1Volume of a solid: the difference of the cylinder readings, or the overflow collected.
2Mass from the balance; density = mass ÷ volume.
3For a liquid, subtract the empty-beaker mass from the total mass.
4Compare with the liquid: lower density floats, higher sinks.
5For hollow objects, use the average density (total mass ÷ total volume).

Measuring the Density of Solids and Liquids; Floating and Sinking in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

A stone in a cylinder

Suppose a stone of mass 54 g is lowered into a cylinder, and the water rises from 30 mL to 50 mL.

Find the density of the stone and say whether it sinks in water.

Try it first, then show the solutionSolution

$V = 50 - 30 = 20$ cm³.
$ρ = \frac{54}{20} = 2.7$ g/cm³.
It is denser than water (1 g/cm³), so it sinks.

Answer: 2.7 g/cm³; the stone sinks.

Memory hook: Denser than water: sinks.

The floating ship

Imagine a steel ship made of a metal sheet with large hollow spaces filled with air.

Why does it float although steel itself is denser than water?

Try it first, then show the solutionSolution

The ship has a very large volume because of the air inside.
Its average density is less than that of water, so it floats.

Answer: The average density (steel plus air) is less than that of water.

Memory hook: Average density decides.

Tricks to remember Measuring the Density of Solids and Liquids; Floating and Sinking

Short memory aids. Say each one aloud once, then use it on a question the same day.

V2 minus V1
Final level minus initial level gives the solid's volume.
Use it when: Cylinder method.
Spout to cylinder
Whatever the solid pushes out of the spout is its volume.
Use it when: Eureka can.
Lighter floats
Float if lighter per volume than the liquid.
Use it when: Floating rule.

Measuring the Density of Solids and Liquids; Floating and Sinking: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Reading the cylinder · 1 mark · MCQBoard level

A stone is lowered into a measuring cylinder; the level rises from 40 mL to 58 mL. The volume of the stone is:
(a) 40 cm³
(b) 58 cm³
(c) 18 cm³
(d) 98 cm³

Try it first, then show the solutionSolution

$V = V_{2} - V_{1} = 58 - 40 = 18$ cm³.

Answer: (c) 18 cm³

Example 2: Why a eureka can? · 2 marks · Short answerBoard level

State the use of a eureka can and describe how it is used to find the volume of a large irregular solid.

Try it first, then show the solutionSolution

It finds the volume of a solid too large for a measuring cylinder. (½)
Fill it to the spout, lower the solid on a thread, collect the overflow in a cylinder: that volume equals the volume of the solid. (1½)

Answer: Overflow volume = solid volume.

Example 3: Density of a key · 3 marks · Short answerHarder board level

A key of mass 39 g is lowered on a thread into a measuring cylinder holding 45 mL of water, and the level reaches 50 mL. Find (a) its volume, (b) its density in g/cm³, (c) its density in kg/m³.

Try it first, then show the solutionSolution

(a) $50 - 45 = 5$ cm³. (1)
(b) $\frac{39}{5} = 7.8$ g/cm³. (1)
(c) $7.8 \times 1000 = 7800$ kg/m³. (1)

Answer: (a) 5 cm³ (b) 7.8 g/cm³ (c) 7800 kg/m³

Example 4: Density of a liquid · 3 marks · Short answerHarder board level

An empty beaker has mass 85 g. With 50 cm³ of a liquid it has mass 125 g. (a) Find the density of the liquid. (b) Will an object of mass 60 g and volume 75 cm³ float in it? (c) Will it float in water?

Try it first, then show the solutionSolution

(a) Mass of liquid $= 40$ g; $ρ = \frac{40}{50} = 0.8$ g/cm³. (1)
(b) Object: $ρ = \frac{60}{75} = 0.8$ g/cm³, equal to the liquid, so it stays where it is placed (neither floats nor sinks). (1)
(c) 0.8 g/cm³ is less than water's 1 g/cm³, so it floats in water. (1)

Answer: (a) 0.8 g/cm³ (b) neither (stays inside) (c) floats

Example 5: The leaking metal box · 4 marks · Case-basedHOTS / competency

A closed hollow metal box has mass 600 g and outer volume 1000 cm³. (a) Find its average density and say whether it floats in water. (b) A leak lets 800 cm³ of water in, filling its empty space. Find the new total mass and average density. (c) Will it float now?

Try it first, then show the solutionSolution

(a) $\frac{600}{1000} = 0.6$ g/cm³, less than 1, so it floats. (1)
(b) Added water mass $= 800$ g (1 g/cm³); total $= 1400$ g. (1)
Average density $= \frac{1400}{1000} = 1.4$ g/cm³. (1)
(c) 1.4 > 1, so it sinks. (1)

Answer: (a) 0.6 g/cm³, floats (b) 1400 g; 1.4 g/cm³ (c) sinks

Where students lose marks in Measuring the Density of Solids and Liquids; Floating and Sinking

The slips examiners see most often, and what to write instead.

Mistake: Reading the top of the meniscus
The bottom of the meniscus gives the correct reading for water.
Wrong working
"Reading at the top edge of the water curve."
Right working
"Reading at the bottom of the curve at eye level."
Do this: Bend down to eye level.
Mistake: Using the mass of the beaker too
The liquid's mass is the difference.
Wrong working
$ρ = \frac{125}{50} = 2.5$ g/cm³.
Right working
$ρ = \frac{125 - 85}{50} = 0.8$ g/cm³.
Do this: Subtract the empty beaker.
Mistake: Floating means "light"
Floating depends on the density, not the mass.
Wrong working
"A heavy log sinks."
Right working
"A log floats if its density is less than water, however heavy."
Do this: Compare densities.

Exam tips

Draw the eureka can and cylinder, labelled, when asked.
Write V = V₂ − V₁ with the units cm³ = mL.
Always compare densities with numbers when deciding float or sink.
For ships and hollow objects talk about the average density.

Practice questions on Measuring the Density of Solids and Liquids; Floating and Sinking

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · Very short answerBoard level
Why is the solid tied to a thread before being lowered into the measuring cylinder?
Hint
Think of splashing.
Answer
So that it can be lowered gently, without splashing water out or breaking the cylinder, and pulled back out.
Q2 · 2 marks · Short answerHarder board level
Ice has a density of about 0.92 g/cm³. Why does ice float on water? What is the practical result for a pond in winter?
Hint
Compare with 1 g/cm³.
Answer
Ice is less dense than water, so it floats. The pond freezes from the top, leaving liquid water below.
Q3 · 3 marks · Short answerHarder board level
List three precautions to take when measuring the volume of an irregular solid with a measuring cylinder.
Hint
Meniscus, eye level, solid.
Answer
Read the bottom of the meniscus at eye level; make sure the solid is completely under water; the solid must not dissolve in or absorb water; lower it gently by a thread to avoid splashing.
Q4 · 3 marks · Short answerHarder board level
A stone of mass 135 g displaces 50 mL of water. (a) Find its density. (b) Will it sink or float in water? (c) Will it float in a liquid of density 3 g/cm³?
Hint
$ρ = \frac{m}{V}$ .
Answer
(a) $\frac{135}{50} = 2.7$ g/cm³. (b) It sinks (2.7 > 1). (c) Yes, it floats, because 2.7 < 3.
Q5 · 4 marks · Long answerHOTS / competency
An egg has a density of 1.08 g/cm³. It is placed in fresh water (1.00 g/cm³), then salt is slowly dissolved until the solution has density 1.20 g/cm³. Describe what happens and at what density it hangs in the middle.
Hint
Compare the egg with the liquid at each stage.
Answer
In fresh water the egg is denser (1.08 > 1.00) and sinks. As salt dissolves the liquid density rises. When it equals 1.08 g/cm³ the egg stays suspended in the middle. When the density rises to 1.20 g/cm³ the egg is less dense than the liquid (1.08 < 1.20) and floats.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.How is the volume of a stone found?Show answer
By displacement of water: V₂ − V₁.
2.What does the eureka can collect?Show answer
The water displaced, equal to the volume of the solid.
3.When does an object float?Show answer
When it is less dense than the liquid.
4.Why does a steel ship float?Show answer
Its average density is less than water.
5.Why does ice float?Show answer
Ice is less dense than water.

Measuring the Density of Solids and Liquids; Floating and Sinking: frequently asked questions

How do you find the volume of an irregular solid?

Lower it into water in a measuring cylinder and subtract the initial reading from the final reading; for a large solid use a eureka can and measure the overflow.

Why do some objects float and others sink?

An object floats if its density is less than that of the liquid and sinks if its density is more.

How does a steel ship float?

The hollow ship contains air, so its average density (steel plus air) is less than the density of water.