This page covers IBPS RRB PO Circles — Area & Circumference with complete concept notes, 9 graded practice MCQs, key points and exam-specific tips. Free to study.
Core ConceptRead this first — the foundation of the topic
Circle is a closed curved shape where all points are equally distant from the center. In SSC CGL, circle questions appear in almost every paper, focusing mainly on area and circumference calculations. Understanding these basics can fetch you 2-3 marks guaranteed.
Key RulesCore rules you must know cold
1
Radius (r): Distance from center to any point on circle
2
Diameter (d): Twice the radius, d = 2r
3
Circumference: Total boundary length of circle
4
Area: Space enclosed within the circle
Formula BlockMemorise — at least one formula appears in every paper
- Circumference = 2πr or πd
- Area = πr²
- If circumference is given, radius = C/(2π)
- If area is given, radius = √(A/π)
Exam PatternsWhat examiners ask — read before attempting PYQs
SSC CGL typically asks direct formula applications, finding one parameter when another is given, and combined problems involving cost calculations. Questions often involve practical scenarios like wire bending, garden fencing, or circular plots.
ShortcutsUse these to save 30–60 seconds per question
#1 - Quick Area from Circumference:
When circumference is given, use this direct formula: Area = C²/(4π)
This saves time by avoiding the step of finding radius first.
Shortcut Trick #2 - Ratio Method:
If radius changes by factor k, then circumference changes by factor k, but area changes by factor k². This helps in comparison problems.
Shortcut Trick #3 - Approximation Technique:
For quick calculations, use π ≈ 22/7 for fractions and π ≈ 3.14 for decimals.
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Find radius using C = 2πr
44 = 2 × (22/7) × r
44 = (44/7) × r
r = 44 × 7/44 = 7 meters
2
Step 2
Calculate area
Area = πr² = (22/7) × 7² = (22/7) × 49 = 22 × 7 = 154 sq meters
Alternative using shortcut:
Area = C²/(4π) = 44²/(4 × 22/7) = 1936/(88/7) = 1936 × 7/88 = 154 sq meters
Worked Example 2:
A wire of length 88 cm is bent to form a circle. If the same wire is bent to form a square, what is the ratio of areas?
1
Step 1
Circle area
Circumference = 88 cm, so radius = 88/(2π) = 88/(2 × 22/7) = 14 cm
Circle area = πr² = (22/7) × 14² = (22/7) × 196 = 616 sq cm
2
Step 2
Square area
Perimeter = 88 cm, so each side = 88/4 = 22 cm
Square area = 22² = 484 sq cm
3
Step 3
Ratio = Circle area : Square area = 616 : 484 = 14 : 11
Most Common Trap - The #1 Mistake:
Students confuse diameter with radius. When a problem states 'circle of 14 cm', always check if it refers to radius or diameter. This single mistake can cost you the entire question. Always read twice and identify clearly whether the given measurement is radius or diameter.
Another frequent error is forgetting to square the radius in area calculations. Students often write Area = πr instead of πr². Practice writing the complete formula every time to
Key Points to Remember
Circumference of circle = 2πr = πd
Area of circle = πr²
Diameter is always twice the radius: d = 2r
Quick area from circumference: Area = C²/(4π)
When radius increases by factor k, area increases by factor k²
Use π = 22/7 for fractions, π = 3.14 for decimals
From area to radius: r = √(Area/π)
From circumference to radius: r = C/(2π)
Always check if given measurement is radius or diameter
Remember to square the radius in area formula, not just multiply
Exam-Specific Tips
Value of π (pi) = 22/7 = 3.14159...
Circle area formula: A = πr² where r is radius
Circle circumference formula: C = 2πr or C = πd
Direct area from circumference: A = C²/(4π)
Ratio of circle area to square area with same perimeter is 14:11
When radius doubles, circumference doubles but area becomes 4 times
Semi-circle area = πr²/2 and perimeter = πr + 2r
In a circle, diameter is the longest chord
Practice MCQs
Circles — Area & Circumference — Practice Questions
9graded MCQs · easy to hard · full solution & trap analysis
The radius of a circle is increased from 7 cm to 14 cm. By what percentage does the area increase? (Use π = 22/7)
Practice 2easy
A circular garden has a radius of 21 m. What is the circumference of the garden? (Use π = 22/7)
Practice 3easy
A circular track has a circumference of 440 m. An athlete runs around it 2.5 times. What distance does the athlete cover? (Use π = 22/7)
Practice 4easy
The circumference of a circle is 88 cm. What is the area of the circle? (Use π = 22/7)
Practice 5medium
A circular pond has a radius of 21 metres. The cost of fencing around the pond is ₹50 per metre. What is the total cost of fencing (in rupees)?
Practice 6medium
Two circles have radii in the ratio 3:4. If the difference between their circumferences is 22 metres, what is the radius of the larger circle?
Practice 7hard
Two circles have areas in the ratio 4:9. A chord of the larger circle is tangent to the smaller circle. If the radius of the smaller circle is 6 cm, what is the distance from the centre of the larger circle to the chord?
Practice 8hard
A circular track has a circumference of 440 metres. A runner completes 2.5 laps in 10 minutes. What is the runner's average speed in km/h?
Practice 9hard
The circumference of a circle is equal to the perimeter of a square with side 11 cm. If the radius of the circle is increased by 50%, what will be the percentage increase in the area of the circle?
60-Second Revision — Circles — Area & Circumference
Formula: Area = πr², Circumference = 2πr
Shortcut: Area from circumference = C²/(4π)
Trap: Always confirm if given value is radius or diameter
Remember: π = 22/7 for fractions, 3.14 for decimals
Quick check: Radius doubles means area becomes 4 times
Formula: From circumference to radius = C/(2π)
Essential: Square the radius for area, don't just multiply