Calculating Arc Length and Circumference

This video tutorial explains how to calculate the arc length of a circle. It begins with an introduction to arcs and their properties, followed by two examples demonstrating the calculation of arc lengths using different radii and central angles. The video also introduces an alternative method using proportions to find arc lengths and circumferences. Key concepts include the relationship between central angles and arcs, and the formula for circumference.

What is an arc in the context of a circle?

• A line connecting two points on the circle's circumference.

• A portion of the circle's circumference.

• The diameter of the circle.

• The center point of the circle.

How do you calculate the arc length of a circle?

• Divide the diameter by the central angle.

• Multiply the radius by the central angle.

• Divide the central angle by 360 and multiply by the circle's circumference.

• Multiply the diameter by Pi (π).

What is the relationship between the central angle and the arc it intercepts?

• They are equal in degrees.

• They are inversely proportional.

• The central angle is half the arc's degree.

• The arc's degree is double the central angle.

What is the arc length when the radius is 8 inches and the central angle is 108 degrees?

• 18.34 inches

• 12.56 inches

• 10.24 inches

• 15.08 inches

How is the circumference of a circle calculated?

• Diameter times Pi (π).

• Radius times Pi (π).

• 2 times radius plus Pi (π).

• 2 times radius times Pi (π).

What is the arc length when the radius is 11 centimeters and the central angle is 60 degrees?

• 7.85 centimeters

• 13.66 centimeters

• 9.42 centimeters

• 11.52 centimeters

What does the new formula for finding arc lengths involve?

• Adding the central angle to the circumference.

• Creating a proportion between the arc length and the circumference.

• Dividing the arc length by the circle's diameter.

• Multiplying the arc length by the circumference.

How do you find the circumference of a circle using the new formula?

• Multiply the arc length by 360 and divide by the central angle.

• Divide the arc length by the central angle and multiply by 360.

• Cross multiply the arc length with 360 and the central angle with the circumference.

• Add the arc length to the central angle and multiply by 360.

What is the circumference of a circle if the arc length is 6 feet and the central angle is 40 degrees?

• 54 feet

• 48 feet

• 60 feet

• 72 feet

What is the purpose of dividing by the circumference in the new formula for arc lengths?

• To convert the arc length into degrees.

• To calculate the radius of the circle.

• To establish a proportion between the arc length and the full circle.

• To find the diameter of the circle.