To find the area of the sector of a circle given the length of the arc and the radius, we can use the following formula:
Area of the sector
First, we need to determine the angle θ in degrees which corresponds to the length of the arc. The formula for the length of an arc (L) is given by:
L = (θ / 360) × 2πr
We know that the arc length L is 4 cm and the radius r is 6 cm. We can rearrange the formula to solve for θ:
θ = (L / (2πr)) × 360
Substituting the known values:
θ = (4 / (2π × 6)) × 360
Now calculating:
θ = (4 / (12π)) × 360 = (1/3π) × 360 = 120°
Now that we have θ, we can find the area of the sector:
A = (120 / 360) × π × (6)²
Calculating:
A = (1/3) × π × 36 = 12π cm²
Therefore, the area of the sector is 12π cm², which is approximately 37.70 cm² when using the value of π as 3.14.