Arc Length and Central Angles

The video tutorial explains the concept of arc length, which is a portion of a circle's circumference. It covers how to calculate arc length using two methods: radians and degrees. The tutorial provides formulas and examples for each method, demonstrating how to find the radius of a circle given the arc length and central angle. The video concludes with a summary of the calculations.

What is arc length in relation to a circle?

• The entire circumference of a circle

• The length of a fraction of the circumference

• The diameter of the circle

• The radius of the circle

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CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

How can the central angle of a circle be measured?

• In seconds or minutes

• In meters or centimeters

• In kilograms or grams

• In radians or degrees

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CCSS.HSG.C.B.5

What is the formula for finding arc length using radians?

• Arc length = radius / angle in radians

• Arc length = radius + angle in radians

• Arc length = radius - angle in radians

• Arc length = radius * angle in radians

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CCSS.HSF.TF.A.1

In the example problem, what was the central angle in radians?

• pi/2

• pi/3

• pi/6

• pi/4

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CCSS.HSG.C.B.5

What is the first step in solving for the radius using arc length in radians?

• Divide both sides by the central angle

• Add the central angle to the arc length

• Multiply both sides by the radius

• Multiply both sides by the central angle

Tags

CCSS.HSG.C.B.5

What is the formula for finding the radius using arc length in degrees?

• Multiply the arc length by the central angle

• Set up a proportion with the central angle over 360 degrees

• Divide the arc length by the central angle

• Set up a proportion with the central angle over 180 degrees

Tags

CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

In the example problem, what was the central angle in degrees?

• 60 degrees

• 120 degrees

• 180 degrees

• 90 degrees

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CCSS.HSG.C.B.5

What is the next step after setting up the proportion in the example problem?

• Add the arc length to the circumference

• Cross multiply to solve for the diameter

• Subtract the arc length from the circumference

• Multiply the arc length by the circumference

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CCSS.7.G.B.4

What is the relationship between diameter and radius?

• Diameter is equal to the radius

• Diameter is half the radius

• Diameter is three times the radius

• Diameter is twice the radius

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CCSS.HSG.C.B.5

What is the final step in finding the radius using the arc length formula in degrees?

• Divide the diameter by two

• Multiply the diameter by two

• Add the diameter to the arc length

• Subtract the diameter from the arc length

Tags

CCSS.HSG.C.B.5