Let's analyze the problem based on the description provided:

You need to order the following parts of a circle according to their areas, in ascending order:

1. The major sector formed by two radii and the major arc AB.
2. The minor sector formed by two radii and the minor arc AB.
3. The major segment formed by line AB and the major arc AB.
4. The minor segment formed by line AB and the minor arc AB.

Key Insights:

• Sectors: These are regions of the circle formed by two radii and the respective arcs.

  • The major sector is the larger area of the two sectors and the minor sector is the smaller area.

• Segments: These are regions of the circle bounded by a chord (in this case, line AB) and the corresponding arc.

  • The major segment is the larger of the two segments formed by line AB and the major arc AB.
  • The minor segment is the smaller of the two segments formed by line AB and the minor arc AB.

Areas:

• The area of a sector depends on the angle subtended by the arc at the center of the circle.

• The major sector will always have a larger area than the minor sector because it spans a larger angle.

• The minor segment will always have a smaller area than the major segment, as it corresponds to a smaller region enclosed by the chord AB and the minor arc.

Ascending order of areas:

1. Minor segment: The smallest area, as it corresponds to the minor arc.
2. Major segment: The larger area than the minor segment, formed by the major arc.
3. Minor sector: The smaller of the two sectors, bounded by the minor arc.
4. Major sector: The largest area, formed by the major arc.

Thus, the correct ascending order is:

1. Minor segment
2. Major segment
3. Minor sector
4. Major sector

Let me know if you need further details or have any questions!

Here are some related questions:

1. How do you calculate the area of a sector?
2. What formula is used to find the area of a circle segment?
3. How can the area of a major sector be compared with a minor sector?
4. What is the relationship between the central angle and the area of a sector?
5. How do the areas of segments relate to the corresponding arcs?

Tip: When comparing sectors and segments, always remember that the sector’s area depends on the angle, while the segment area depends on both the angle and the length of the chord.