Exploring Circumference and Area of Circles

This video tutorial covers the second part of the 8.7 notes on circles. It begins with a review of key circle concepts such as radius, diameter, and circumference, and explains the relationship between circumference and pi. The tutorial then introduces central angles and sectors, providing definitions and examples. The main focus is on calculating the area of a sector using a proportion formula, with a detailed example demonstrating the process. The video concludes with a practice exercise for students.

What is the term used to describe the distance from the center of a circle to its perimeter?

• Sector

• Radius

• Circumference

• Diameter

Which number is commonly used to approximate pi?

• 5.14

• 4.14

• 3.14

• 2.14

How can the circumference of a circle be calculated using the diameter?

• Pi times the diameter

• Two times the radius

• Pi plus the diameter

• Pi divided by the diameter

What is the formula to calculate the area of a circle?

• Pi times the diameter squared

• Two times pi times the radius

• Pi times the radius squared

• Pi divided by the radius

What is a central angle in a circle?

• An angle with its vertex on the circle

• An angle with its vertex at the center of the circle

• An angle formed outside the circle

• An angle formed by two tangents

What is a sector in a circle?

• A line that touches the circle at one point

• The outer edge of the circle

• The longest chord of the circle

• The area enclosed by two radii and an arc

What two pieces of information are needed to calculate the area of a sector?

• The diameter and the circumference

• The circumference and the radius

• The radius and the central angle

• The diameter and the central angle

What is the formula setup for finding the area of a sector?

• Circle area times sector area equals 360 times central angle

• Sector area times circle area equals central angle times 360

• Sector area over circle area equals central angle over 360

• Circle area over sector area equals 360 over central angle

How is the area of the entire circle represented in the sector area formula?

• Pi times radius

• Pi times diameter squared

• Pi times radius squared

• Two times pi times radius

In the example, if the central angle is 120 degrees and the radius is 10 cm, what is the area of the sector?

• Approximately 120 square centimeters

• Approximately 100 square centimeters

• Approximately 314 square centimeters

• Approximately 105 square centimeters