A circle has an area of 36 in2. What is the area of a sector of the circle that has a central angle of
π/6 ?
A) 3 in2
B) 6 in2
C) 12 in2
D) 196 in2
I think Its 12
x/(π/6) = 36/2π
x = (π/6)(36/(2π))
= 3 in^2
To find the area of a sector of a circle, you can use the formula:
Area of Sector = (Central Angle / 2π) * π * r^2,
where r is the radius of the circle.
Given that the area of the circle is 36 in², we can find the radius (r) using the formula for the area of a circle:
Area of Circle = π * r^2.
36 in² = π * r^2.
Divide both sides by π:
r^2 = 36 in² / π.
Taking the square root of both sides:
r = √(36 in² / π).
Now, we can substitute the value of r into the formula for the area of the sector:
Area of Sector = (π/6 / 2π) * π * (√(36 in² / π))^2.
Simplifying:
Area of Sector = (1/12) * π * (36 in² / π).
Canceling out π:
Area of Sector = (1/12) * 36 in².
Simplifying:
Area of Sector = 3 in².
Therefore, the area of the sector with a central angle of π/6 is 3 in².
So, the correct answer is A) 3 in².
To find the area of a sector, you need to know the formula for the area of a sector and then apply it to the given information.
The formula for the area of a sector is:
Area of sector = (θ/2π) * πr^2,
where θ is the central angle in radians and r is the radius of the circle.
In this case, the central angle is π/6, and the area of the circle is given as 36 in2.
To find the radius of the circle, we can use the formula for the area of a circle:
Area of circle = πr^2.
In this case, the area of the circle is 36 in2. So we can solve for r as follows:
36 = πr^2,
r^2 = 36/π,
r = √(36/π).
Now that we have the radius, we can substitute the values into the formula for the area of the sector:
Area of sector = (π/6)/(2π) * π(√(36/π))^2.
Simplifying the expression:
Area of sector = (1/12) * π * (36/π),
Area of sector = 3 in2.
Therefore, the area of the sector with a central angle of π/6 is 3 in2 (option A).