1
Circumference = 2πr
Area = πr²
2
Arc length = πr
Area = ½πr²
3
Arc length = ½πr
Area = ¼πr²
4
Area = π(R² − r²)
FORMULA CHAPTER
Chapter 18 – Area of a Circle
WBBSEClass 09Mathematics4 formulas
Complete WBBSE Madhyamik Class 9 Area of a Circle formula list covering circles, semicircles, quadrants and circular rings with worked examples.
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Circle Circumference and Area
Circumference = 2πr
Area = πr²
SymbolMeaningUnit
rRadius of the circlelength units
πCircle constant, approximately 22/7 or 3.1416Not applicable
CircumferenceLength around the circlelength units
AreaRegion inside the circlesquare units
Worked example
Question: Find the circumference and area of a circle of radius 7 cm, using π = 22/7.
Calculation:
Step 1: Circumference = 2 × 22/7 × 7 = 44 cm.
Step 2: Area = 22/7 × 7² = 154 cm².
Answer: Circumference = 44 cm and area = 154 cm².
Semicircle Arc Length and Area
Arc length = πr
Area = ½πr²
SymbolMeaningUnit
rRadius of the semicirclelength units
Arc lengthCurved half-circumferencelength units
AreaArea of the semicirclesquare units
Worked example
Question: Find the curved arc length and area of a semicircle of radius 14 cm, using π = 22/7.
Calculation:
Step 1: Arc length = 22/7 × 14 = 44 cm.
Step 2: Area = ½ × 22/7 × 14² = 308 cm².
Answer: Arc length = 44 cm and area = 308 cm².
Quadrant Arc Length and Area
Arc length = ½πr
Area = ¼πr²
SymbolMeaningUnit
rRadius of the quadrantlength units
Arc lengthCurved quarter-circumferencelength units
AreaArea of the quadrantsquare units
Worked example
Question: Find the curved arc length and area of a quadrant of radius 14 cm, using π = 22/7.
Calculation:
Step 1: Arc length = ½ × 22/7 × 14 = 22 cm.
Step 2: Area = ¼ × 22/7 × 14² = 154 cm².
Answer: Arc length = 22 cm and area = 154 cm².
Area of a Circular Ring
Area = π(R² − r²)
SymbolMeaningUnit
ROuter radiuslength units
rInner radiuslength units
AreaArea of the circular ringsquare units
Worked example
Question: Find the area of a circular ring with outer radius 7 cm and inner radius 5 cm, using π = 22/7.
Calculation:
Step 1: R² − r² = 7² − 5² = 49 − 25 = 24.
Step 2: Area = π(R² − r²).
Step 3: Area = 22/7 × 24 = 528/7 cm².
Answer: The area is 528/7 cm², approximately 75.43 cm².