Finding Arc Length: Techniques and Examples

Mr. Dow introduces the concept of arc length, comparing it to the crust of a pizza slice. He explains two methods of measuring arc length: by degrees and by distance. The video demonstrates how to calculate arc length using proportions, given the central angle and radius. Three examples are provided: finding arc length, determining the central angle, and calculating the radius. The video emphasizes the practical application of these calculations in real-world scenarios.

What are the two methods of measuring arc length?

• By radius and diameter

• By degrees and by distance

• By volume and mass

• By circumference and area

What is required to calculate the arc length by distance?

• The diameter and the circumference

• The volume of the sphere

• The central angle and the radius

• The area of the circle

Tags

CCSS.HSG.C.B.5

What is the relationship between the central angle and the measure of the arc in degrees?

• There is no direct relationship

• They are equal

• The measure of the arc is half the central angle

• The central angle is twice the measure of the arc

Tags

CCSS.HSG.C.B.5

What is the practical use of measuring arc length in terms of distance?

• To find the diameter of a circle

• To calculate the volume of a sphere

• To measure the length of a pizza crust

• To determine the height of a circle

How is the proportion set up to find the arc length?

• Central angle over 360 equals arc length over 2πr

• Arc length over central angle equals 360 over 2πr

• Central angle over arc length equals 2πr over 360

• Arc length over 2πr equals central angle over 360

Tags

CCSS.HSG.C.B.5

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

• πd

• 2πr

• 2r

• πr^2

Tags

CCSS.7.G.B.4

What do you need to know to calculate the arc length in terms of distance?

• The diameter and the circumference

• The radius and the central angle

• The area of the circle

• The volume of the sphere

Tags

CCSS.HSG.C.B.5

What does the proportion of the central angle over 360 degrees to arc length over the circumference represent?

• The ratio of the circle's volume to its surface area

• The ratio of the arc's length to the circle's total circumference

• The ratio of the circle's diameter to its radius

• The ratio of the circle's area to its circumference

Tags

CCSS.HSG.C.B.5

How do you find the central angle when given the arc length and radius?

• Multiply the arc length by 360 and divide by 2πr

• Divide the arc length by the radius and multiply by 360

• Multiply the arc length by 2πr and divide by 360

• Divide the arc length by 2πr and multiply by 360

Tags

CCSS.HSG.C.B.5

How can you find the radius of a circle given the arc length and the central angle?

• Multiply the arc length by the central angle and divide by 2π

• Divide 360 times the arc length by the product of 2π and the central angle

• Divide the arc length by 2π and multiply by the central angle

• Divide the arc length by the central angle and multiply by 360

Tags

CCSS.HSG.C.B.5