Calculating Arc Length and Sector Area

This video tutorial covers the concept of arc length, explaining its practical applications and how to calculate it using both degrees and radians. The instructor provides a detailed breakdown of the formula for circumference and demonstrates how to apply it to find the arc length of a circle. Several examples are worked through, including advanced calculations using radians and fractions. The tutorial concludes with a brief introduction to the next topic, sector area, which will be covered in the following video.

What is the formula for the circumference of a circle?

• C = r^2π

• C = πd

• C = 2r

• C = 2πr

How do you calculate the arc length for half of a circle?

• Divide the circumference by 4

• Multiply the circumference by 2

• Multiply the circumference by 0.5

• Divide the circumference by 2

What is the general formula for calculating arc length?

• Arc length = (θ/360) × πd

• Arc length = (θ/360) × 2πr

• Arc length = (θ/180) × πr

• Arc length = θ × r

How do you calculate arc length using radians?

• Arc length = (θ/2π) × 2πr

• Arc length = θ × r

• Arc length = (θ/π) × πr

• Arc length = θ × 2πr

What is the arc length when the angle is 270 degrees and the radius is 13 feet?

• 61.3 feet

• 19.25π feet

• 75.4 feet

• 24π feet

How is the arc length calculated when given in radians, specifically 3π/2?

• Arc length = 3π/2 × r

• Arc length = 2π × r

• Arc length = π × r

• Arc length = r/2π

What is the arc length when the angle is 90 degrees and the radius is 13 feet?

• 6.8 inches

• 26π feet

• 13π feet

• 6.5π feet

If the radius of a circle is 16 feet and the angle is 3π/2 radians, what is the arc length?

• 24π feet

• 32π feet

• 48π feet

• 8π feet

What is the result of calculating the arc length for an angle of 150 degrees and a radius of 19 feet, without rounding?

• 7π feet

• 19.25π feet

• 60.5 feet

• 95π/6 feet

For an angle of π/2 radians and a radius of 14, what is the arc length?

• 3.5π centimeters

• 28π centimeters

• 14π centimeters

• 7π centimeters