Chapter 1 of 19

Tamil Nadu (TNBSE)Class 7 Science★ 6-10 marks in the TN Class 7 Term 1 exam through area, volume and density questions

Measurement

Samacheer Kalvi (TN State Board) Class 7 Science — Term 1 Chapter 1, Measurement. Fundamental and derived quantities, area, volume (including the volume of a cylinder and of irregular solids by displacement), and density and its unit, with the actual book-back questions, common mistakes and quick revision.

⏱ 15 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Define area and state its SI unit
2Calculate the volume of regular solids
3Measure the volume of an irregular solid by displacement
4Apply the density formula
5Predict floating and sinking from density

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Why this chapter matters

Measuring area, volume and density is the foundation of all experimental science. The displacement method and the density formula are directly tested in the TN Class 7 Term 1 exam.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Class 6 — Measurement

Length, mass and units.

Measurement — Class 7 Science (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 7 Science, Term 1 — Chapter 1. Area, volume and density.

1. About this chapter

This chapter covers fundamental and derived quantities, area, volume (including the volume of irregular solids by displacement), and density and its unit.

2. Fundamental and derived quantities

Fundamental quantities are basic (length, mass, time); derived quantities are got from them — area, volume and density are derived quantities.

3. Area and volume

Area is the surface covered, in square units; the SI unit of area is m². Area of a rectangle = length × breadth.
Volume is the space occupied, in cubic units; the SI unit is m³. 1 L = 1000 cc (cm³) and 1 m³ = 10⁶ cm³.
Volume of a cylinder = πr²h; volume of a cuboid = l × b × h.
The volume of an irregular solid is found using the law of displacement of water: volume = final − initial water level.

4. Density

Density = mass ÷ volume; its SI unit is kg/m³ (also g/cm³).
An object sinks if its density is greater than the liquid's (an iron ball sinks in water because iron is denser than water) and floats if it is less.

5. Worked examples

Example 1. Name the derived quantities in this chapter. Area, volume and density.

Example 2. A stone raises the water level from 50 mL to 65 mL. Find its volume. 65 − 50 = 15 cm³.

Example 3. A body of mass 200 g has volume 25 cm³. Find its density. 200 ÷ 25 = 8 g/cm³.

6. Book-back questions (Samacheer Kalvi)

I. Choose the correct answer

Which of the following is a derived unit? — (a) mass / (b) length / (c) area. Ans: (c) area.
The SI unit of density is — (a) g/cm³ / (b) kg/m³. Ans: (b) kg/m³.
A light year is a unit of — (a) distance / (b) time. Ans: (a) distance.
Two spheres have equal mass and their volumes are in the ratio 2 : 1. The ratio of their densities is — (a) 1 : 2 / (b) 2 : 1. Ans: (b) 2 : 1 (smaller volume → greater density).

II. Fill in the blanks 5. The volume of an irregularly shaped object is measured using the law of displacement. 6. One cubic metre is equal to 10⁶ (one million) cubic centimetres. 7. 1 litre = 1000 cubic centimetres.

III. Answer briefly 8. Name some derived quantities. — Area, volume and density. 9. Write the formula for the volume of a cylinder. — V = πr²h. 10. Name a liquid in which an iron ball sinks, and why. — Water; iron is denser than water, so it sinks.

7. Common mistakes

Mistake: Calling area or volume a fundamental quantity. Fix: Area, volume and density are derived quantities.
Mistake: Forgetting to subtract readings in the displacement method. Fix: Volume of an irregular solid = final − initial water level.
Mistake: Writing density without units. Fix: Density = mass ÷ volume, in kg/m³ or g/cm³.

8. Quick revision

Term 1 · Ch 1 · measurement.
Derived quantities: area (m²), volume (m³), density (kg/m³).
1 L = 1000 cc; 1 m³ = 10⁶ cm³; volume of a cylinder = πr²h.
Irregular solid by the law of displacement; density = mass ÷ volume; iron sinks in water.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Area

rectangle = l × b; SI unit m²

Square units.

Volume

cuboid = l × b × h; SI unit m³

1 L = 1000 cm³.

Irregular solid

volume = final − initial water level

Displacement method.

Density

density = mass ÷ volume (g/cm³)

Floats if < liquid density.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Giving area in cubic units or volume in square units

✓ Area is in square units; volume is in cubic units.

WATCH OUT

✗ Forgetting to subtract readings in the displacement method

✓ Volume of an irregular solid = final − initial water level.

WATCH OUT

✗ Writing density without units

✓ Density = mass ÷ volume, in g/cm³ or kg/m³.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Choose the correct answer

Book-back MCQs on derived units, density, light year and density ratio.

Questions

Fill in the blanks

Law of displacement, 1 m³ in cm³ and 1 litre in cc.

Questions

Answer briefly

Derived quantities, cylinder volume and floating/sinking.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· MCQ

Which of the following is a derived unit: mass, length or area?

▶ Show solution

Area (it is derived from length).

Q2EASY· MCQ

The SI unit of density is ____.

▶ Show solution

kg/m³.

Q3EASY· Fill in the blanks

The volume of an irregularly shaped object is measured using the law of ____.

▶ Show solution

displacement.

Q4MEDIUM· MCQ

Two spheres have equal mass and volumes in the ratio 2 : 1. Find the ratio of their densities.

▶ Show solution

2 : 1 (for equal mass, density is inversely related to volume).

Q5MEDIUM· Density

A body of mass 200 g has volume 25 cm³. Find its density.

▶ Show solution

200 ÷ 25 = 8 g/cm³.

Q6EASY· Answer briefly

Name a liquid in which an iron ball sinks and explain why.

▶ Show solution

Water; iron is denser than water, so the iron ball sinks.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Term 1 Chapter 1 of Samacheer Kalvi Class 7 Science.
•Area = surface covered (SI unit m²); rectangle area = l × b.
•Volume = space occupied (SI unit m³; 1 L = 1000 cm³); cuboid = l × b × h.
•Volume of an irregular solid = final − initial water level (displacement method).
•Density = mass ÷ volume (g/cm³ or kg/m³).
•An object floats if its density is less than the liquid's, and sinks if greater.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 6-10 marks across area, volume and density

Question type	Marks each	Typical count	What it tests
Objective	1	3-4	Units and simple sums
Displacement	2	1	Irregular-solid volume
Density	2	1-2	Density and floating

Prep strategy

Keep area square and volume cubic units
Use final − initial for displacement
Memorise density = mass ÷ volume
Compare densities for floating/sinking

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Shipping

Ships float because their overall density is less than water.

Cooking

Measuring volumes of liquids in millilitres.

Quality testing

Density checks the purity of materials.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Always write the correct unit (square or cubic)
Use final − initial for displacement
State the density formula before substituting
Compare densities to decide floating

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

A cube of side 2 cm has mass 24 g. Find its density and whether it floats on water.
Explain how a hydrometer uses density.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 7 Term 1 ExamHigh

NMMS / Foundation ScienceMedium

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

By the displacement method: note the water level in a measuring cylinder, drop in the solid, note the new level, and the rise in level equals the volume of the solid.

An object floats if its density is less than that of the liquid and sinks if its density is greater — which is why wood floats on water but iron sinks.

Practice more, ask doubts, find a tutor

Tamil Nadu (TNBSE) Class 7 mock tests

Tamil Nadu (TNBSE) Class 7 PYQs

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Science flashcards

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