Understanding Circles: Circumference and Arc Length

This video tutorial covers the second part of the unit on circles, focusing on circumference and arc length. It explains the concept of circumference, providing formulas for calculation using both radius and diameter. The tutorial also delves into arc length, distinguishing it from arc measure, and demonstrates how to calculate it as a fraction of the circle's circumference. The video includes examples and practice problems, offering strategies for solving both forward and backward problems related to these concepts.

What is the formula for the circumference of a circle using its diameter?

• d/2

• πr²

• πd

• 2πr

How is arc length different from arc measure?

• Arc length and arc measure are the same.

• Arc length is always larger than arc measure.

• Arc length is measured in degrees, while arc measure is in radians.

• Arc length is a part of the circumference, while arc measure is an angle.

Which formula can be used to calculate the arc length of a circle?

• Arc measure/360 × r

• Arc measure/360 × d

• Arc measure/360 × 2πr

• Arc measure/360 × πr²

If a circle has a radius of 5 and an angle of 50 degrees, what is the arc length?

• 5π

• 10π

• 50π/36

• 25π/18

What is the first step in solving a backwards problem involving arc length?

• Calculate the diameter.

• Find the radius.

• Multiply the arc length by π.

• Use the proportion of the measure over 360 equals arc length over circumference.

In a backwards problem, if the arc length is 12 and the angle is 85 degrees, what is the next step after setting up the proportion?

• Subtract the angle from 360.

• Add the arc length to the circumference.

• Divide by the angle measure.

• Cross multiply to solve for circumference.

What is the circumference of a circle with a diameter of 15?

• 7.5π

• 15π

• 45π

• 30π

If the radius of a circle is 20, what is its circumference?

• 20π

• 40π

• 80π

• 10π

How do you find the length of an arc if the angle is 90 degrees and the diameter is 14?

• Multiply 14 by π and divide by 6

• Multiply 14 by π and divide by 8

• Multiply 14 by π and divide by 2

• Multiply 14 by π and divide by 4

What is the arc length of a circle with a 120-degree angle and a diameter of 12?

• 4π

• 6π

• 10π

• 8π