Arc Length and Diameter Calculations

The video tutorial explains how to find the diameter of a circle using the arc length of a slice of quiche. The problem is set up by dividing the quiche into eight equal slices, with the arc length of one slice given as 6.28 inches. The tutorial guides through the process of using proportions to relate the arc length to the circumference, and then solving for the diameter using cross multiplication and division. The final result is approximated to 16 inches.

What is the main objective of the problem discussed in the video?

• To find the radius of a quiche slice

• To determine the diameter of a quiche slice

• To calculate the area of a quiche slice

• To measure the thickness of a quiche slice

Tags

CCSS.HSG.C.B.5

What is the arc length of one slice of the quiche?

• 3.14

• 6.28

• 12.56

• 9.42

Tags

CCSS.HSG.C.B.5

Which formula is used to relate arc length and circumference?

• Measure over 360

• Diameter over radius

• Measure over 180

• Area over circumference

Tags

CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

How many degrees is one slice of the quiche?

• 90°

• 45°

• 30°

• 60°

Tags

CCSS.7.G.B.4

What is the circumference of a circle in terms of diameter?

• 2πr

• πd

• d/π

• r/2π

Tags

CCSS.7.G.A.1

What operation is performed to solve for the diameter after setting up the proportion?

• Cross multiplication

• Subtraction

• Division

• Addition

Tags

CCSS.6.NS.B.3

What is the result of multiplying 8 by 6.28 in the calculation?

• 50.24

• 502.4

• 5.024

• 5024

Tags

CCSS.HSG.GPE.A.1

What is the approximate diameter of the quiche slice?

• 17

• 14

• 15.99

• 16

What is the final step to find the diameter after calculating the cross product?

• Add π

• Multiply by π

• Divide by π

• Subtract π

Tags

CCSS.7.G.B.4

Which option represents the best choice for the diameter in the context of the problem?

• 14 in

• 15 in

• 17 in

• 16 in

Tags

CCSS.7.G.B.4