Area of a Segment of a Circle

Area of a Segment of a Circle

Read each question carefully and calculate the area of the segment of the circle. Show all your work and round your answers to two decimal places where necessary.

1. A circle has a radius of 10 cm. Find the area of the segment formed by a central angle of 60 degrees. (Use π = 3.14 and √3 = 1.73)

2. Calculate the area of the segment of a circle with a radius of 12 inches and a central angle of 90 degrees. (Use π = 3.14)

3. The formula for the area of a sector of a circle is A = (θ/360) * πr², where θ is the central angle in degrees and r is the  .

4. To find the area of a segment, you subtract the area of the   from the area of the sector.

5. A segment of a circle is the region bounded by an arc and two radii.

6. The area of a triangle formed by two radii and a chord can be calculated using 0.5 * r² * sin(θ).

7. A circular garden has a radius of 15 meters. A path is built along a chord that subtends a central angle of 120 degrees. What is the area of the smaller segment of the garden? (Use π = 3.14 and √3 = 1.73)