Understanding Circle Properties and Arc Length

The video tutorial explains a geometry problem involving two concentric circles. It starts by identifying the center and given measurements, then calculates the radii of both circles. The tutorial demonstrates how to find the circumference of the smaller circle and explains the proportional relationship between radius and circumference. Finally, it calculates the arc length of a specific section of the smaller circle using the given angle.

What is the relationship between the radii of the larger and smaller circles?

• The radius of the larger circle is half that of the smaller circle.

• The radii of both circles are equal.

• The radius of the smaller circle is half that of the larger circle.

• The radius of the smaller circle is twice that of the larger circle.

How do you calculate the radius of the larger circle given its circumference?

• Multiply the circumference by pi.

• Divide the circumference by two pi.

• Multiply the circumference by two pi.

• Divide the circumference by pi.

If the circumference of a circle is 36, what is the radius?

• 36/pi

• 9/pi

• 18/pi

• 72/pi

What is the formula for the circumference of a circle?

• pi times the radius

• two pi times the radius

• pi times the diameter

• two pi times the diameter

What is the radius of the smaller circle if the larger circle's radius is 18/pi?

• 36/pi

• 27/pi

• 18/pi

• 9/pi

What is the circumference of the smaller circle?

• 27

• 9

• 18

• 36

How is the circumference of a circle related to its radius?

• Circumference is inversely proportional to the radius.

• Circumference is directly proportional to the radius.

• Circumference is directly proportional to the square of the radius.

• Circumference is unrelated to the radius.

What fraction of the circle does the 80-degree arc represent?

• 1/4

• 1/3

• 1/5

• 1/6

How do you calculate the arc length of a circle?

• Subtract the fraction of the circle represented by the arc from the circumference.

• Add the circumference to the fraction of the circle represented by the arc.

• Divide the circumference by the fraction of the circle represented by the arc.

• Multiply the circumference by the fraction of the circle represented by the arc.

What is the arc length of the 80-degree section of the smaller circle?

• 4

• 8

• 16

• 12