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 area of a sector of a circle is given by the formula A = (θ/360)πr^2, where A is the area of the sector, r is the radius of the circle, and θ is the central angle of the sector in degrees. We are given that the radius of the circle is 7cm and the area of the sector is 44cm^2, so we can plug these values into the formula:
44 = (θ/360)(22/7)(7)^2
Simplifying this expression, we get:
44 = (θ/360)(22)(7)
44 = (77θ/180)
θ = (180/77)(44)
θ ≈ 102.6 degrees
Therefore, the angle of the sector is approximately 103 degrees to the nearest degree, which is.