The diameter of circle C is 18 cm. measurement of arc AD is 60°. Use this information, the diagram, and your experiences in geometry this semester to answer these questions. (Use 3.14 as pie)

area of sector is 60/360 * 81pi

arc length subtended is 60/360 * 18pi

For any other questions, you're on your own...

To answer these questions, let's start by examining the given information and the diagram.

We are told that the diameter of circle C is 18 cm. This means that the distance across the circle passing through its center is 18 cm.

We are also given that the measurement of arc AD is 60°. An arc is a curved segment of a circle, and in this case, arc AD is the part of the circle between points A and D. The measurement of an arc is typically given in degrees, which tell us the angle formed by the two radii (lines from the center of the circle to the endpoints of the arc) that intersect at the center of the circle.

With these details in mind, let's address the questions:

1. What is the circumference of circle C?
To find the circumference of a circle, we can use the formula C = πd, where C is the circumference and d is the diameter. In this case, we have the diameter (18 cm), so we can substitute it into the formula: C = 3.14 * 18 cm. Simplifying this, we get C ≈ 56.52 cm (rounded to two decimal places).

2. What is the length of arc AD?
To find the length of an arc, we can use the formula L = (θ/360) * C, where L is the length of the arc, θ is the measure of the arc in degrees (in this case, 60°), and C is the circumference of the circle. Substituting the values into the formula: L = (60°/360°) * 56.52 cm. Simplifying this, we get L ≈ 9.42 cm (rounded to two decimal places).

3. What is the area of the sector AOC?
The sector of a circle is like a slice that is formed by two radii and an arc. To find the area of a sector, we use the formula A = (θ/360) * πr^2, where A is the area, θ is the measure of the central angle in degrees (in this case, 60°), and r is the radius of the circle. Since we have the diameter (18 cm), we can calculate the radius by dividing it by 2: r = 18 cm / 2 = 9 cm. Substituting the values into the formula: A = (60°/360°) * 3.14 * (9 cm)^2. Simplifying this, we get A ≈ 47.70 cm^2 (rounded to two decimal places).

By using the given information and applying the appropriate formulas from geometry, we were able to determine the circumference of circle C, the length of arc AD, and the area of sector AOC.