Understanding Circles: Circumference and Arc Length

This video tutorial covers the second part of the circles unit, focusing on circumference and arc length. It explains the concept of circumference, provides formulas for calculation, and demonstrates examples. The tutorial also introduces arc length, differentiating it from arc measure, and provides examples of calculating arc length. Additionally, it covers solving problems by working backwards, offering a simplified approach using proportions.

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

• d/π

• 2πr

• πd

• πr²

If the radius of a circle is 14.3 inches, what is the diameter?

• 14.3 inches

• 43.9 inches

• 28.6 inches

• 7.15 inches

How is arc length different from arc measure?

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

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

• Arc length is a fixed value, while arc measure changes with circle size.

• Arc length is the entire circumference, while arc measure is a part of it.

What is the formula for calculating arc length?

• Arc measure/360 * πd

• Arc measure/180 * 2πr

• Arc measure/360 * 2πr

• Arc measure/180 * πd

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

• 10π inches

• 25π/18 inches

• 50π/36 inches

• 5π inches

What is the simplified form of 170/12π?

• 85/12π

• 170/24π

• 170/6π

• 85/6π

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

• Calculate the circumference using πd.

• Find the radius using 2πr.

• Multiply the arc length by the diameter.

• Use the proportion of arc measure over 360.

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

• Cross multiply to solve for circumference.

• Divide the arc length by the angle.

• Add the arc length to the circumference.

• Subtract the angle from 360.

What is the circumference if Dπ equals 50.82?

• 50.82

• 85

• 12

• 360

Which formula can be used interchangeably with Dπ in arc length calculations?

• 2πr

• πr²

• d/π

• r/2π