Find the area of a sector bounded by a 60 degrees central angle in a circle of radius 6 inches
since a = 1/2 r^2 θ, just plug in
π/3 and 6, and calculate
a = (1/2)(36)(π/3) = 6π
3/2pi
Well, let's put our clown hats on and calculate the area of that sector, shall we? 🎪
The formula to find the area of a sector is:
Area of sector = (θ/360) * π * r^2
Where θ is the central angle in degrees, r is the radius of the circle, and π is the mathematical constant.
Using the given values, we have:
Central angle (θ) = 60 degrees
Radius (r) = 6 inches
Plugging these values into the formula, we get:
Area of sector = (60/360) * π * (6^2)
Simplifying further, we have:
Area of sector = (1/6) * π * 36
Now, multiplying, we get:
Area of sector ≈ (1/6) * 3.14159 * 36
Approximating the value of π to 3.14159, we have:
Area of sector ≈ (1/6) * 3.14159 * 36 ≈ 18.8495559215 square inches
So, the area of the sector is approximately 18.85 square inches. Keep clownin' around with math! 🤡
To find the area of a sector of a circle, you can use the formula:
A = (θ/360) * π * r^2
Where:
A = Area of the sector
θ = Central angle of the sector
r = Radius of the circle
Substituting the given values:
θ = 60 degrees
r = 6 inches
A = (60/360) * π * 6^2
Simplifying this equation:
A = (1/6) * π * 36
A = (1/6) * 36π
A = 6π
Therefore, the area of the sector bounded by a 60-degree central angle in a circle with a radius of 6 inches is 6π square units.
To find the area of a sector, you can use the formula:
Area = (θ/360) × πr²
Where:
- θ is the central angle
- r is the radius of the circle
In this case, the central angle is 60 degrees and the radius is 6 inches. Let's substitute these values into the formula and calculate the area:
Area = (60/360) × π(6)²
Area = (1/6) × π(36)
Area = (1/6) × 36π
Area = 6π square inches
Therefore, the area of the sector bounded by a 60-degree central angle in a circle with a radius of 6 inches is 6π square inches.