Question
Download Solution PDFAn arc of length 23.1 cm subtends an 18° angle at the centre. What is the area of the circle? [Use \(π = \frac{22}{7}\)]
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Length of an arc = 23.1 cm
Angle subtended on center by arc = 18°
Formula used:
Length of an arc = (2 × π × R × θ)/360
Area of circle = π × R2
Where, R = radius
Calculation:
Length of an arc = (2 × π × R × θ)/360
⇒ 23.1 = (2 × 22 × R × 18)/(360 × 7)
⇒ 23.1 = (22 × R)/(10 × 7)
⇒ R = (2.1 × 70)/2 = 73.5 cm
Area of circle = π × R2
⇒ (22/7) × 73.5 × 73.5
⇒ 22 × 10.5 × 73.5
⇒ 16978.50 cm2
∴ The correct answer is 16978.50 cm2.
Last updated on Jul 19, 2025
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