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Tamil Nadu (TNBSE)Class 7 Mathematics★ 6-10 marks in the TN Class 7 Term 2 exam through circumference, area and pathway sums

Measurements (Term 2) - Circles

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 2 Chapter 2, Measurements (Circles). The parts of a circle, the circumference (C = 2πr) and area (A = πr²) of a circle, and the area of pathways (rings) between two circles, with worked examples, exercises and quick revision.

⏱ 14 min readEasy difficulty✓ Free · NCERT-aligned

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Key points, glossary and the questions most likely to show up.

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

1Name the parts of a circle
2Calculate the circumference of a circle
3Calculate the area of a circle
4Find a missing radius from circumference or area
5Find the area of a circular pathway

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Why this chapter matters

Circles appear in wheels, plates, gardens and design. The circumference and area formulae and pathway problems are directly tested in the TN Class 7 Term 2 exam.

Before you start — revise these

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

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Term 1 — Measurements (Area and Perimeter)

Area and perimeter basics.

Measurements (Circles) — Class 7 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 7 Mathematics, Term 2 — Chapter 2. Circumference, area and circular pathways.

1. About this chapter

This chapter covers the basic concept of a circle, the circumference and area of a circle, and the area of pathways (circular rings).

2. Parts of a circle

The centre is the fixed middle point; the radius (r) is the distance from the centre to the edge; the diameter (d) = 2r passes through the centre.
The circumference is the boundary length of the circle.
π (pi) ≈ 22/7 or 3.14 is the ratio of circumference to diameter.

3. Circumference and area

Quantity	Formula
Circumference	C = 2πr = πd
Area	A = πr²

4. Area of a pathway

A circular pathway is the ring between an outer circle (radius R) and an inner circle (radius r).
Area of the pathway = πR² − πr² = π(R² − r²).

5. Worked examples

Example 1. Find the circumference of a circle of radius 7 cm (π = 22/7). C = 2πr = 2 × 22/7 × 7 = 44 cm.

Example 2. Find the area of a circle of radius 7 cm. A = πr² = 22/7 × 7 × 7 = 154 cm².

Example 3. A circular path has outer radius 14 m and inner radius 7 m. Find its area (π = 22/7). Area = π(R² − r²) = 22/7 × (196 − 49) = 22/7 × 147 = 462 m².

6. Exercises (Samacheer Kalvi)

Find the circumference of a circle of radius 21 cm.
Find the area of a circle of diameter 28 cm.
The circumference of a circle is 66 cm. Find its radius.
A circular garden of radius 35 m has a 7 m wide path around it. Find the area of the path.
Find the area of a circle whose radius is 10 cm (π = 3.14).

7. Common mistakes

Mistake: Using the diameter as the radius. Fix: r = d/2; use the radius in the formulas.
Mistake: Mixing up circumference and area. Fix: C = 2πr (linear units); A = πr² (square units).
Mistake: Subtracting radii instead of areas for a pathway. Fix: Pathway area = π(R² − r²), not π(R − r)².

8. Quick revision

Term 2 · Ch 2 · circles.
d = 2r; π ≈ 22/7 or 3.14.
Circumference C = 2πr = πd; area A = πr².
Pathway (ring) area = π(R² − r²).

Key formulas & results

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

Diameter

d = 2r

Through the centre.

Circumference

C = 2πr = πd

Boundary length.

Area

A = πr²

Square units.

Pathway (ring)

π(R² − r²)

Outer minus inner area.

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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

✗ Using the diameter as the radius

✓ r = d/2; always use the radius in the formulas.

WATCH OUT

✗ Mixing up circumference and area

✓ C = 2πr (linear units); A = πr² (square units).

WATCH OUT

✗ Subtracting radii instead of areas for a pathway

✓ Pathway area = π(R² − r²), not π(R − r)².

NCERT exercises (with solutions)

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

Circumference

Find circumference; find radius from circumference.

Questions

Area

Find area; find radius from area.

Questions

Pathways

Area of circular rings/paths.

Questions

Practice problems

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

Q1EASY· Circumference

Find the circumference of a circle of radius 21 cm (π = 22/7).

▶ Show solution

2 × 22/7 × 21 = 132 cm.

Q2EASY· Area

Find the area of a circle of diameter 28 cm (π = 22/7).

▶ Show solution

r = 14; A = 22/7 × 14 × 14 = 616 cm².

Q3MEDIUM· Reverse

The circumference of a circle is 66 cm. Find its radius (π = 22/7).

▶ Show solution

2 × 22/7 × r = 66 → r = 10.5 cm.

Q4MEDIUM· Pathway

A circular garden of radius 35 m has a 7 m wide path around it. Find the area of the path (π = 22/7).

▶ Show solution

R = 42, r = 35; π(R² − r²) = 22/7 × (1764 − 1225) = 22/7 × 539 = 1694 m².

Q5EASY· Area

Find the area of a circle of radius 10 cm (π = 3.14).

▶ Show solution

3.14 × 100 = 314 cm².

Q6EASY· Concept

What is the value of π as a fraction?

▶ Show solution

22/7 (approximately).

5-minute revision

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

•Term 2 Chapter 2 of Samacheer Kalvi Class 7 Maths.
•Centre, radius (r), diameter (d = 2r), circumference and π (≈ 22/7).
•Circumference C = 2πr = πd (linear units).
•Area A = πr² (square units).
•Find a missing radius by rearranging the formula.
•Area of a circular pathway = π(R² − r²).

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 circle and pathway sums

Question type	Marks each	Typical count	What it tests
Circumference	2	1-2	Boundary length
Area	2	2	Area of a circle
Pathway	3	1	Ring area

Prep strategy

Convert diameter to radius first
Pick π = 22/7 when the radius is a multiple of 7
Keep circumference and area formulas distinct
For paths, subtract the inner area from the outer area

Where this shows up in the real world

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

Wheels and discs

Distance covered by a wheel uses its circumference.

Gardens and tracks

Paths around circular lawns use ring areas.

Design

Plates, clocks and logos are circular.

Exam strategy

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

State the formula before substituting
Convert diameter to radius
Use the convenient value of π
Subtract areas (not radii) for pathways

Going beyond the textbook

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

A wheel of radius 35 cm rolls 100 times. Find the distance covered.
Two concentric circles have radii 9 cm and 12 cm. Find the ring area.

Where else this chapter is tested

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

TN Class 7 Term 2 ExamHigh

NMMS / Foundation MathsMedium

School unit testsHigh

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Questions students ask

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

Use 22/7 when the radius or diameter is a multiple of 7 (the 7s cancel neatly); otherwise 3.14 is usually easier.

The pathway is the difference of two circular areas, so you subtract the inner area πr² from the outer area πR², giving π(R² − r²).

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