This page covers SSC GD Constable Circles — Area & Circumference with complete concept notes, 16 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
16graded MCQs · easy to hard · full solution & trap analysis
A circle has a diameter of 14 m. What is its area? (Use π = 22/7)
Practice 2easy
The circumference of a circle is 88 cm. What is its radius? (Use π = 22/7)
Practice 3easy
The area of a circle is 616 cm². What is its diameter? (Use π = 22/7)
Practice 4easy
A circular garden has a radius of 10.5 m. What is its circumference? (Use π = 22/7)
Practice 5easy
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 6easy
The radius of a circle is 7 cm. What is its circumference? (Use π = 22/7)
Practice 7medium
Two circles have radii in the ratio 3:4. What is the ratio of their circumferences?
Practice 8medium
A circular track has a circumference of 440 m. A runner starts at point A and runs along the track. After running 330 m, what angle (in degrees) has the runner covered with respect to the centre of the circle? (Use π = 22/7)
Practice 9medium
The area of a circle is 616 cm². What is its circumference? (Use π = 22/7)
Practice 10medium
A wheel has a diameter of 70 cm. How many complete revolutions will it make to cover a distance of 2.2 km? (Use π = 22/7)
Practice 11medium
The circumference of a circle is 88 cm. If the radius is increased by 50%, what will be the percentage increase in the circumference? (Use π = 22/7)
Practice 12hard
The circumference of a circle is 88 cm. A sector of this circle has a central angle of 45°. What is the area of the sector (in cm²)?
Practice 13hard
Two concentric circles have radii 7 cm and 5 cm respectively. A chord of the larger circle is tangent to the smaller circle. Find the length of this chord.
Practice 14hard
Two circles have areas in the ratio 4:9. If the circumference of the smaller circle is 44 cm, what is the circumference of the larger circle (in cm)?
Practice 15hard
The area of a circle is 616 cm². If a concentric circle has a radius that is 50% larger, what is the difference in their circumferences (in cm)?
Practice 16hard
A circular track has a radius of 35 m. A runner completes 8 full laps. If the runner then runs an additional arc covering a central angle of 72°, what is the total distance covered (in metres)?
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