Calculating Arc Length and Sector Area

This video tutorial explains how to calculate the arc length and sector area of a circle when the angle is given in degrees. It provides formulas for both calculations, demonstrates examples, and offers practice questions with solutions. The video emphasizes the use of degrees rather than radians and guides viewers through the process of applying the formulas to find the arc length and sector area.

What is the formula to calculate the circumference of a circle?

• C = 2 * pi * r

• C = pi * r^2

• C = 2 * r

• C = pi * d

How do you find the proportion of the circle's circumference that corresponds to a given angle in degrees?

• Divide the angle by 360

• Multiply the angle by 360

• Divide 360 by the angle

• Multiply the angle by 2 * pi

What unit of measurement is used for arc length?

• Square centimeters

• Meters

• Cubic centimeters

• Centimeters

If a sector of a circle has an angle of 105 degrees and a radius of 7 cm, what is the arc length?

• 10.5 cm

• 22.5 cm

• 15.7 cm

• 12.8 cm

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

• A = pi * r^2

• A = 2 * pi * r

• A = 2 * r^2

• A = pi * d^2

How do you calculate the area of a sector given its angle in degrees and radius?

• Divide the circle's area by 360

• Multiply the circle's area by the angle divided by 360

• Divide the circle's area by the angle

• Multiply the circle's area by the angle

If a sector's angle is 105 degrees and the radius is 7 cm, what is the sector area?

• 39.2 cm^2

• 50 cm^2

• 47.5 cm^2

• 44.9 cm^2

What is the correct way to express the area of a sector?

• In radians

• In linear units

• In square units

• In cubic units

For an angle of 105 degrees and radius of 7 cm, what fraction of the circle's area does the sector cover?

• 105/7

• 360/105

• 7/105

• 105/360

What is the result of calculating the sector area with an angle of 105 degrees and a radius of 7 cm?

• 39.2 cm^2

• 50 cm^2

• 44.9 cm^2

• 47.5 cm^2