A sector of a circle has a radius 5cm
The area of the sector is 5π
Work out the arc length
s = rθ
so, what's θ?
1/2 r^2 θ = 5π
To find the arc length of the sector, we can use the formula:
Arc Length = (Sector Angle / 360°) * Circumference of the Circle
To find the sector angle, we can use the formula for the area of a sector:
Area of Sector = (Sector Angle / 360°) * π * (Radius^2)
Given that the area of the sector is 5π and the radius is 5cm, we can set up the equation:
5π = (Sector Angle / 360°) * π * (5^2)
Simplifying the equation, we have:
5π = (Sector Angle / 360°) * 25π
We can cancel out the π terms on both sides of the equation:
5 = Sector Angle / 360° * 25
To isolate the Sector Angle, we multiply both sides of the equation by (360° / 25):
Sector Angle = 5 * (360° / 25)
Simplifying further:
Sector Angle = 5 * 14.4°
Sector Angle = 72°
Now that we have the Sector Angle, we can find the arc length using the formula:
Arc Length = (Sector Angle / 360°) * Circumference of the Circle
The circumference of a circle can be calculated using the formula:
Circumference = 2 * π * Radius
Substituting the values, we have:
Circumference = 2 * π * 5
Circumference = 10π
Now we can calculate the arc length:
Arc Length = (72° / 360°) * 10π
Arc Length = (0.2) * 10π
Arc Length = 2π
Therefore, the arc length of the sector is 2π cm.