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AFCAT Circles — Area & Circumference

Study Material — 4 PYQs (2018–2020) · Concept Notes · Shortcuts

AFCAT Circles — Area & Circumference is a frequently tested subtopic — 4 previous year questions from 2018–2020 papers are included below with concept notes, key rules and shortcut tricks.

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2018–2020
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Previous Year Questions

AFCAT Circles — Area & Circumference — Past Exam Questions

4 questions from actual AFCAT papers · all shown free · click option to reveal solution

Exam Q 12018Previous Year Pattern

The radius of a circle is 7 cm. What is the area of the circle? (Use π = 22/7)

Exam Q 22020Previous Year Pattern

A circular garden has a radius of 14 metres. What is the difference between its circumference and diameter?

Exam Q 32018Previous Year Pattern

A circular park has a circumference of 176 m. A man jogs along a path that is 7 m inside the boundary of the park. What is the area (in m²) of the jogging path strip between the boundary and the jogging track? (Use π = 22/7)

Exam Q 42020Previous Year Pattern

A circular park has a circumference of 88 metres. A path of uniform width 2 metres is constructed inside the park along its boundary. Find the area of the path (in square metres).

Concept Notes

Circles — Area & Circumference— Rules & Concept

1.Core Concept

Read this first — the foundation of the topic

CIRCLES — AREA & CIRCUMFERENCE CORE CONCEPT

A circle is a simple closed shape where every point on the boundary is the same distance from the center. That fixed distance is called the RADIUS (r). The distance across the circle through the center is the DIAMETER (d = 2r). Circles appear in almost every SSC CGL paper — sometimes directly, sometimes inside triangles, squares, or other shapes.

2.Key Rules

Core rules you must know cold
1

The boundary of a circle is called its CIRCUMFERENCE — think of it as the perimeter of the circle.

2

Pi (π) is a fixed constant ≈ 22/7 or 3.14. Use 22/7 when the radius is a multiple of 7. Use 3.14 for decimals.

3

If radius doubles, area becomes 4 times. If radius triples, area becomes 9 times. Area grows as the square of the radius.

4

A semicircle is half a circle. Its perimeter = πr + 2r (curved part + diameter).

5

A quadrant is one-fourth of a circle. Its perimeter = (πr/2) + 2r.

3.Formula Block

Memorise — at least one formula appears in every paper
Circumference = 2πr = πd
- Area = πr²
- Area in terms of diameter = π(d/2)² = πd²/4
- Area in terms of circumference (C): Area = C²/4π
- Radius in terms of circumference: r = C/2π
- Semicircle Area = πr²/2
- Semicircle Perimeter = πr + 2r
- Ring Area (two concentric circles) = π(R² - r²) where R = outer radius, r = inner radius

4.Exam Patterns

What examiners ask — read before attempting PYQs
1

Direct: Find area or circumference given radius or diameter.

2

Reverse: Find radius given area or circumference.

3

Ratio-based: If radius increases by X%, find % increase in area.

4

Combined shapes: Circle inscribed in a square, or square inscribed in a circle.

5

Ring/Annulus problems: Two concentric circles.

6

Sector and arc problems (linked to angles).

5.Shortcuts

Use these to save 30–60 seconds per question
Example

C = 44. Area = (44 × 44)/(4 × 22/7) = 1936/(88/7) = 1936 × 7/88 = 154 sq units

TRICK 3 — Circle Inscribed in Square

If a circle is inscribed in a square of side a → radius = a/2. If a circle is circumscribed around a square of side a → radius = a√2/2 = a/√2.

6.Worked Example

Solve this step-by-step before moving on
1
Step 1

Circumference = 2πr → 88 = 2 × (22/7) × r

2
Step 2

r = 88 × 7 / (2 × 22) = 616/44 = 14 cm

3
Step 3

Area = πr² = (22/7) × 14 × 14 = (22/7) × 196 = 22 × 28 = 616 sq cm Answer: 616 sq cm WORKED EXAMPLE 2 Q: The radius of a circle is increased by 20%. By what percent does the area increase?

1
Step 1

Use the trick formula: % increase in area = 2r + r²/100 where r = 20%

2
Step 2

= 2(20) + (20 × 20)/100 = 40 + 4 = 44% Answer: Area increases by 44% Verification: Old area = πR². New radius = 1.2R. New area = π(1.2R)² = 1.44πR². Increase = 44%. Confirmed!

7.Exam Traps

Common mistakes students make — avoid these

— THE NUMBER ONE TRAP Students confuse RADIUS and DIAMETER. Many questions give the diameter but students use it directly as the radius in the formula. Always check: is the number given the radius or the diameter?

If diameter is given, divide by 2 first before applying any formula. This single mistake causes maximum wrong answers in circle problems.

Key Points to Remember

  • Circumference of a circle = 2πr = πd (use π = 22/7 when radius is multiple of 7)
  • Area of a circle = πr² (area depends on the SQUARE of the radius)
  • If radius doubles, area becomes 4 times; if radius triples, area becomes 9 times
  • Shortcut: If radius increases by r%, area increases by (2r + r²/100)%
  • Shortcut: Area = C²/4π — find area directly from circumference without finding radius
  • Ring/Annulus area = π(R² - r²) where R is outer radius and r is inner radius
  • Circle inscribed in square of side a → radius = a/2; diameter = a
  • Circle circumscribed around square of side a → radius = a√2/2
  • Semicircle perimeter = πr + 2r (curved arc + straight diameter, NOT just πr)
  • Trap: Always check if the value given is RADIUS or DIAMETER before substituting in formula

Exam-Specific Tips

  • The value of π used in SSC exams is 22/7 (when radius is a multiple of 7) or 3.14 (for decimal-based questions)
  • Area of a circle with circumference C is given by the formula: C²/4π
  • A 10% increase in radius leads to exactly 21% increase in area (using the formula 2r + r²/100)
  • A 20% increase in radius leads to exactly 44% increase in area
  • For a circle inscribed in a square of side 'a': radius = a/2 and area of circle = πa²/4
  • For a square inscribed in a circle of radius r: side of square = r√2 and area of square = 2r²
  • Area of semicircle = πr²/2 and its perimeter = r(π + 2)
Practice MCQs

Circles — Area & Circumference — Practice Questions

41graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 41

All MCQs →
Practice 1easy

A wheel has a radius of 35 cm. How many complete revolutions will it make to cover a distance of 2200 m? (Use π = 22/7)

Practice 2easy

The radius of a circle is 7 cm. What is its circumference? (Use π = 22/7)

Practice 3easy

The area of a circle is 154 cm². What is its circumference? (Use π = 22/7)

Practice 4easy

A circle has a diameter of 14 m. Find its area. (Use π = 22/7)

Practice 5easy

Two circles have radii 5 cm and 12 cm respectively. What is the difference between their areas? (Use π = 22/7)

Practice 6easy

Two circles have radii 5 cm and 3 cm respectively. What is the difference between their areas? (Use π = 3.14)

Practice 7easy

A circular garden has a radius of 21 m. What is the area of the garden? (Use π = 22/7)

Practice 8easy

The area of a circle is 154 cm². What is its circumference? (Use π = 22/7)

Practice 9easy

A circular garden has a radius of 14 metres. A path of width 2 metres is constructed around the outer edge of the garden. What is the difference between the area of the garden including the path and the area of the garden alone? (Use π = 22/7)

Practice 10easy

The radius of a circle is 7 cm. What is the area of the circle? (Use π = 22/7)

Practice 11easy

A circle has a diameter of 14 m. Find its area. (Use π = 22/7)

Practice 12easy

A wheel has a diameter of 35 cm. How many complete revolutions will it make to cover a distance of 1100 m? (Use π = 22/7)

Practice 13easy

The radius of a circle is 7 cm. What is its circumference? (Use π = 22/7)

Practice 14easy

The circumference of a circle is 88 cm. What is its radius? (Use π = 22/7)

Practice 15easy

A circular park has a circumference of 220 m. What is the area of the park? (Use π = 22/7)

Practice 16easy

A circular garden has an area of 616 m². What is its circumference? (Use π = 22/7)

Practice 17easy

The circumference of a circle is 44 cm. What is its radius? (Use π = 22/7)

Practice 18easy

A circular garden has a radius of 21 m. What is the area of the garden? (Use π = 22/7)

Practice 19easy

The circumference of a circle is 88 cm. What is its radius? (Use π = 22/7)

Practice 20medium

A wheel has a radius of 35 cm. How many complete revolutions will it make to cover a distance of 2.2 km? (Use π = 22/7)

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60-Second Revision — Circles — Area & Circumference

  • Formula: Circumference = 2πr; Area = πr². Use π = 22/7 when r is a multiple of 7.
  • Shortcut: % increase in area when radius increases by r% → use (2r + r²/100). No long calculation needed.
  • Shortcut: Area from circumference directly → Area = C²/4π. Saves time in reverse problems.
  • Remember: Semicircle perimeter = πr + 2r (students often forget to add the diameter 2r).
  • Trap: If question gives DIAMETER, divide by 2 first to get radius before using any formula.
  • Ring area = π(R² − r²). Factor it as π(R+r)(R−r) for faster calculation.
  • Circle in square → r = a/2. Circle around square → r = a√2/2. Memorise both for combined shape questions.
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