Understanding Sector Area and Arc Length

The video tutorial covers solving application problems using sector area and arc length. It begins with a problem involving a pie cut into six equal pieces, where the arc length of one piece is given. The tutorial demonstrates drawing the problem, understanding the central angle, and using the proportion method to find the circumference and diameter of the pie. The solution involves calculating the circumference using the arc length and central angle, then finding the diameter by dividing the circumference by Pi.

What is the first step in solving the problem of finding the pie's diameter?

• Draw a picture of the pie and its slices.

• Calculate the circumference directly.

• Measure the pie's radius.

• Find the area of the pie.

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

• 90 degrees

• 60 degrees

• 45 degrees

• 30 degrees

What method is used to relate the arc length to the circumference?

• Radius Method

• Diameter Method

• Proportion Method

• Area Method

What is the formula used to find the circumference in the Proportion Method?

• Arc length / Circumference = Angle / 270 degrees

• Arc length / Circumference = Angle / 180 degrees

• Arc length / Circumference = Angle / 360 degrees

• Arc length / Circumference = Angle / 90 degrees

What is the circumference of the pie calculated using the Proportion Method?

• 28.4 cm

• 30.4 cm

• 32.4 cm

• 34.4 cm

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

• Multiply the circumference by Pi.

• Divide the circumference by Pi.

• Subtract Pi from the circumference.

• Add Pi to the circumference.

What is the final diameter of the pie?

• 10.31 cm

• 12.31 cm

• 9.31 cm

• 11.31 cm