How do you find arc length and area

Question

How do you find arc length subtended by a central angle of 30degrees?
How do you find the Area of a sector of the circle formed by an angle of 30degrees?

Answer 1

1.Arc length of circle : s = Ѳ(π/180)r

central angle(Ѳ) = 30º

A radian is mesure of an angle Ѳ, substands an arc whose lenth equals the lenght  of the radius of the circle (r) = 1

s =30(π/180)(1)

s = 30(180/180)

s = 30(1)

s = 30

Answer 2

2. Area of sector of the circle =( n/360 )πr²

Where n is number of degrees in central angle of the sector (n) = 30º

A radian is measure of an angle Ѳ, subtends an arc whose length equals the length  of the radius of the circle (r) = 1

= (30/360)180(1)

= 30/2

= 15

Area of sector of the circle = 15

Comments

The length of the arc : L = (θ/360) * 2πr, where θ = central angle and r = radius.

Central angle θ = 30.

L = (30/360) * 2πr = πr / 6 radians.

 

The area of the sector : A = (θ/360) * πr², where θ = central angle and r = radius.

Central angle θ = 30.

A = (30/360) * πr² = πr² / 12 square units.