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- A = (θ/360) * π * r² - (1/2) * r² * sin(θ) Where: A represents the area of the segment. θ denotes the central angle of the segment in degrees. π (pi) is a constant approximately equal to 3.14159. r signifies the radius of the circle. sin(θ) calculates the sine of the central angle θ, achievable using a scientific calculator or software.
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Formula To Calculate Area of a Segment of a Circle; Area of a Segment in Radians: A = (½) × r 2 (θ – Sin θ) Area of a Segment in Degrees: A = (½) × r 2 × [(π/180) θ – sin θ]
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What Is the Formula for Area of the Segment of a Circle? The area of the segment of the circle (or) minor segment of a circle is: (θ / 360°) × πr 2 - (1/2) r 2 sin θ (OR) r 2 [πθ/360° - sin θ/2], if 'θ' is in degrees (1/2) × r 2 θ - (1/2) r 2 sin θ (OR) (r 2 / 2) [θ - sin θ], if 'θ' is in radians
May 24, 2024 · You can calculate the segment area in three steps: Determine the radius of the circle. Calculate the central angle. Apply the segment area formula: 0.5 × r² × (α – sin(α))
Aug 3, 2023 · Area (A) of a Segment of a Circle = ½ × r2 × (πθ /180 – sin θ) Thus, if the radius is known and the central angle of the segment is given in degrees, the formula to find the area of a segment is given below. Segment of a Circle Formula. Let us solve some examples to understand the concept better.
Jun 15, 2022 · A segment of a circle is the area of a circle that is bounded by a chord and the arc with the same endpoints as the chord. The area of a segment is \(A_{\text{segment}}=A_sector−A_{\Delta ABC}\) Figure \(\PageIndex{2}\)
Area of Segment = θ − sin(θ)2 × r 2 (when θ is in radians) Area of Segment = ( θ × π 360 − sin(θ)2) × r 2 (when θ is in degrees) Arc Length. The arc length (of a Sector or Segment) is: L = θ × r (when θ is in radians) L = θ × π 180 × r (when θ is in degrees)
( A B) 2 = 100. ∴ ( O A) 2 + ( O B) 2 = ( A B) 2 ∠ AOB = 90. Area of sector OAB = 90 360 × 22 7 × ( 50) 2 = 39.29 c m 2. Area of triangle OAB = 1 2 r 2 s i n θ = 1 2 × (50 sin 90) = 25 c m 2. ∴ Area of Minor Segment = Area of sector OAB – Area of triangle OAB. = 39.29 – 25 = 14.29 c m 2.
