A sector of a circle of radius 7cm has an area of 44cm2. Calculate the angle of the sector correct to the nearest degree [Take π = 22/7]
Answer Details
The formula for the area of a sector is: A = (θ/360)πr2 where A is the area of the sector, θ is the angle of the sector in degrees, r is the radius of the circle, and π is the mathematical constant pi. We are given that the radius of the circle is 7cm and the area of the sector is 44cm2. Substituting these values into the formula above, we get: 44 = (θ/360) × (22/7) × 72 Simplifying this equation, we get: 44 = (θ/360) × 22 × 7 44 = (θ/360) × 154 Multiplying both sides by 360, we get: θ = (44 × 360) / 154 θ = 102.597 Rounding to the nearest degree, we get: θ ≈ 103o Therefore, the angle of the sector correct to the nearest degree is 103o. Answer is correct.