An arc subtends an angle 15 degrees at the centre of the circle. If the radius is 4 centimetres, find the area of the sector?
Thanks Reiny. it was simpl right?
To find the area of the sector, we need to use the formula:
Area of Sector = (θ/360) * π * r^2
Where:
θ = Central angle in degrees
r = Radius of the circle
In this case, the central angle (θ) is given as 15 degrees, and the radius (r) is given as 4 centimeters.
Substituting these values into the formula:
Area of Sector = (15/360) * π * (4^2)
≈ (0.0417) * π * 16
≈ 0.5236 * 16
≈ 8.3776 square centimeters
Therefore, the area of the sector is approximately 8.3776 square centimeters.
area of whole circle = 16π cm^2
15° = 1/24 of a rotation, so the are of the sector is
(1/24)(16π) = 2π/3 cm^2