This page covers SBI PO Circles — Area & Circumference with complete concept notes, 12 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
12graded MCQs · easy to hard · full solution & trap analysis
A circular garden has a radius of 21 metres. What is the cost of fencing it at ₹5 per metre?
Practice 2easy
A circular track has a circumference of 220 metres. An athlete runs 5 complete laps. What is the total distance covered? (Use π = 22/7)
Practice 3easy
The radius of a circle is 7 cm. What is its circumference? (Use π = 22/7)
Practice 4easy
A circle has a diameter of 14 metres. Find its area. (Use π = 22/7)
Practice 5easy
The circumference of a circle is 44 cm. What is its radius? (Use π = 22/7)
Practice 6medium
A sector of a circle with radius 21 cm has a central angle of 120°. What is the area of the sector (in cm²)?
Practice 7medium
A circular garden has a circumference of 88 metres. A path of width 2 metres is constructed around the garden on the outside. What is the area of the path (in square metres)?
Practice 8medium
A circular track has a circumference of 440 metres. A runner completes 2.5 laps around the track. What is the area enclosed by the track (in m²)?
Practice 9medium
A circular pond has a radius of 35 metres. The cost of fencing around the pond is ₹50 per metre. What is the total cost of fencing (in ₹)?
Practice 10hard
A circular track has a circumference of 440 m. A runner completes 2.5 laps in 10 minutes. If the runner maintains the same speed, how many complete laps will be covered in 1 hour?
Practice 11hard
Two circles have radii 6 cm and 8 cm. The distance between their centres is 10 cm. What is the length of the direct common tangent (external tangent) to both circles?
Practice 12hard
A circular garden has a radius of 21 m. A path of uniform width 3.5 m is laid around the inside of the garden (i.e., between the inner and outer boundaries of the path). If the cost of laying the path is ₹50 per m², what is the total cost?
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