Understanding Arc Length and Diameter

The video tutorial explains how to find the diameter of a pie cut into six equal pieces, given the arc length of one piece. The teacher guides through drawing the pie, understanding the division of the circle, and using the proportion method to calculate the circumference. Finally, the diameter is determined by working backwards from the circumference.

What is the arc length of one piece of the pie?

• 5.0 cm

• 5.4 cm

• 6.0 cm

• 4.5 cm

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CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

How many degrees is the central angle of each piece of the pie?

• 30 degrees

• 90 degrees

• 60 degrees

• 45 degrees

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CCSS.1.G.A.3

What fraction of the circle does each piece of the pie represent?

• 1/6

• 1/8

• 1/5

• 1/4

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CCSS.HSG.C.B.5

What is the proportion method used for in this problem?

• To calculate the diameter directly

• To relate arc length to circumference

• To measure the central angle

• To find the area of the pie

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CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

What is the total angle of a circle?

• 90 degrees

• 360 degrees

• 270 degrees

• 180 degrees

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CCSS.6.NS.B.3

What is the result of multiplying 6 by 5.4 in the context of this problem?

• 34.4

• 28.4

• 30.4

• 32.4

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CCSS.7.G.A.1

What does the variable X represent in the proportion method?

• Circumference

• Radius

• Diameter

• Area

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CCSS.7.G.B.4

How is the diameter of the pie calculated from the circumference?

• By subtracting pi

• By multiplying by pi

• By adding pi

• By dividing by pi

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CCSS.7.G.B.4

What is the final calculated diameter of the pie?

• 10.31 cm

• 11.31 cm

• 12.31 cm

• 9.31 cm

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CCSS.2.MD.A.2

In what unit is the diameter of the pie expressed?

• Millimeters

• Centimeters

• Meters

• Inches

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CCSS.2.MD.A.2