in a circle of radius 11 cm, find the area of the segment bounded by an arc of measure 60 degrees and the chord joining the endpoints of the arc.

A. 12.9 cm
B. 122.5 cm
C. 11.0 cm
D. none of these

3.14(11^2)/6 - 2(11)5.5/2

= 63.355 - 60.5 = 2.855 sqcm

Therefore, D.

area of segment of circle

To find the area of the segment bounded by an arc of measure 60 degrees and the chord joining the endpoints of the arc, we can follow these steps:

1. Calculate the area of the sector: The sector is formed by the arc and two radii of the circle. The formula to find the area of a sector is (θ/360) * π * r^2, where θ is the measure of the arc in degrees, and r is the radius of the circle.
In this case, θ = 60 degrees and r = 11 cm, so the area of the sector is (60/360) * π * 11^2 = (1/6) * π * 121 = (121/6) * π.

2. Calculate the area of the triangle: The triangle is formed by the chord and two radii of the circle. To find the area of the triangle, we need to calculate the length of the chord.
In a circle, the chord subtended by an angle θ at the center is given by the formula 2 * r * sin(θ/2), where r is the radius of the circle.
In this case, θ = 60 degrees and r = 11 cm, so the length of the chord is 2 * 11 * sin(60/2) = 22 * sin(30) = 22 * (1/2) = 11 cm.
The area of the triangle is (1/2) * base * height = (1/2) * 11 * 11 = 121/2 cm^2.

3. Subtract the area of the triangle from the area of the sector to get the area of the segment: Area of the segment = Area of the sector - Area of the triangle = (121/6) * π - 121/2.

Now, let's calculate the area of the segment using the formulas:

Area of the segment = (121/6) * π - 121/2 = 20.1667 π - 60.5
≈ 63.6179 cm^2

Therefore, the correct answer is not provided among the options given (D. none of these).