FIND THE LENGTH OF THE RADIUS OF THE CIRCLE IS 9cm. THE ARC OF THE SECTOR MEASURES 60 DEGREES. FIND THE AREA OF THE SECTOR.
Area of the sector=PI*radius^2*angle/360
the angle which is two times its complement
To find the area of the sector, we will need to find the length of the arc and the length of the radius.
Given:
Radius of the circle = 9 cm
Arc of the sector = 60 degrees
Step 1: Calculate the circumference of the circle.
The formula for the circumference of a circle is C = 2πr, where r is the radius.
C = 2π(9) = 18π cm
Step 2: Calculate the length of the arc.
The formula for the length of an arc is L = (θ/360) × C, where θ is the angle in degrees and C is the circumference of the circle.
L = (60/360) × 18π = (1/6) × 18π = 3π cm
Step 3: Calculate the area of the sector.
The formula for the area of a sector is A = (θ/360) × πr², where θ is the angle in degrees and r is the radius.
A = (60/360) × π(9)² = (1/6) × π(81) = (27/2)π cm²
So, the area of the sector is (27/2)π cm².
To find the area of the sector, we first need to find the length of the arc. The formula to find the length of an arc is given by:
Length of arc = (θ/360) * 2πr
where θ is the central angle of the sector in degrees and r is the radius of the circle.
Given that the radius of the circle is 9 cm and the arc of the sector measures 60 degrees, we can substitute these values into the formula:
Length of arc = (60/360) * 2π(9)
= (1/6) * 2π(9)
= (1/6) * 18π
= 3π cm
Next, to find the area of the sector, we can use the formula:
Area of sector = (θ/360) * πr^2
Substituting the given values:
Area of sector = (60/360) * π(9)^2
= (1/6) * π(81)
= (π/6) * 81
= 13.5π cm^2
Therefore, the area of the sector is 13.5π square cm.