Calculating Arc Length and Sector Area with Proportions

This video tutorial teaches how to calculate the length of an arc and the area of a sector using proportions. It explains the concept of using the central angle theta in relation to the full circle's 360 degrees to find the arc length and sector area. The tutorial provides examples, demonstrating the proportion method and alternative formulas. It also covers solving for unknown central angles when given arc length and radius, and briefly mentions working with radians.

What is the ratio of the central angle to the total degrees in a circle?

• Theta to 270 degrees

• Theta to 360 degrees

• Theta to 180 degrees

• Theta to 90 degrees

What is the relationship between the part and the whole in the proportion method?

• Part plus whole equals whole

• Whole divided by part equals part

• Part to whole equals part to whole

• Part minus whole equals whole

How do you find the length of an arc using proportions?

• Multiply the central angle by the radius

• Divide the central angle by 360 and multiply by 2πr

• Add the central angle to the circumference

• Subtract the central angle from the circumference

What does the formula θ/360 * 2πr calculate?

• Area of the sector

• Circumference of the circle

• Diameter of the circle

• Length of the arc

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

• (Theta/360) / πr^2

• (Theta/360) - πr^2

• (Theta/360) * πr^2

• (Theta/360) + πr^2

If a sector's central angle is 90 degrees and the radius is 4, what is the sector's area?

• 12π inches squared

• 8π inches squared

• 4π inches squared

• 16π inches squared

If the central angle is 135 degrees and the radius is 10 cm, what is the arc length?

• 10π/2 cm

• 5π/2 cm

• 20π/2 cm

• 15π/2 cm

If the central angle is 135 degrees and the radius is 10 cm, what is the area of the sector?

• 75π/2 cm^2

• 50π/2 cm^2

• 25π/2 cm^2

• 100π/2 cm^2

How do you solve for the central angle given the arc length and radius?

• Multiply arc length by radius and divide by 2π

• Divide arc length by the circumference and multiply by 360

• Add arc length to the circumference and divide by radius

• Subtract arc length from the circumference and multiply by radius

What is the central angle if the arc length is 18 and the radius is 10?

• Approximately 103 degrees

• Approximately 150 degrees

• Approximately 90 degrees

• Approximately 120 degrees