Find the area of a segment of a circle, in which the radius of the circle it is in, is 6cm, and the central angle measures 120 degrees. Round your answer to the nearest tenth.
The radius of a circle is 7 feet. What is the area of a sector bounded by a 180° arc?
To find the area of a segment of a circle, you can use the formula:
Area of a Segment = (θ/360) * π * r^2
Where:
- θ is the central angle of the segment,
- π is a mathematical constant approximately equal to 3.14159,
- r is the radius of the circle.
In this case, the radius of the circle is given as 6cm, and the central angle is 120 degrees. Plugging these values into the formula:
Area of the Segment = (120/360) * π * (6cm)^2
Area of the Segment = (1/3) * π * 36cm^2
Area of the Segment ≈ 12.6cm^2
Therefore, the area of the segment of the circle, rounded to the nearest tenth, is approximately 12.6 square centimeters.
Ac = pi*r^2 = 3.14*6^2 = 113.1 cm^2. =
Area of circle.
As = (120/360) * 113.1 = 37.7 cm^2. =
Area of segment.