solve this---**Question Number:** 34 **Diagram Description:** * Type: Circle with a shaded sector. * Center: Labeled as point C. * Circle: A complete circle is shown. * Shaded Region: A sector of the circle is shaded. * Angle: The central angle of the shaded sector is 100°, with the vertex at the center C. **Question Stem:** Point C is the center of the circle above. What fraction of the area of the circle is the area of the shaded region?

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In this problem, we have a circle with center C. A sector of the circle is shaded, and the central angle of this sector is 100 degrees. We need to find what fraction of the circle's area is represented by the shaded region. To solve this problem, we need to find what fraction of the full circle is represented by the sector. Since the central angle of the sector is 100 degrees, and a full circle is 360 degrees, the fraction is 100 divided by 360. Simplifying this fraction, we get 5/18. Therefore, the shaded region is 5/18 of the circle's area. To solve this problem, we need to find what fraction of the full circle is represented by the sector. Since the central angle of the sector is 100 degrees, and a full circle is 360 degrees, the fraction is 100 divided by 360. To simplify this fraction, we first divide both numerator and denominator by 10, getting 10 over 36. Then we divide both by 2, resulting in 5 over 18. Therefore, the shaded region is 5/18 of the circle's area. Let's visualize how the fraction of the circle changes as the central angle changes. When the central angle is 100 degrees, the sector represents 100/360 of the circle's area, which simplifies to 5/18 or approximately 27.8 percent. This relationship is direct - the fraction of the area equals the fraction of the total angle. If we were to increase the angle to 180 degrees, we would have half the circle. At 360 degrees, we would have the entire circle. Now let's look at how to calculate the actual area of the sector. The area of a circle is pi times radius squared. The area of a sector is the fraction of the central angle divided by 360 degrees, multiplied by the area of the circle. For our 100-degree sector, the area is 100 divided by 360, times pi r squared, which simplifies to 5/18 times pi r squared. When we find the ratio of the sector area to the circle area, the pi r squared terms cancel out, leaving us with 5/18. This confirms our earlier result that the shaded region is 5/18 of the circle's area. Let's summarize what we've learned. The fraction of a circle's area occupied by a sector equals the fraction of the central angle to 360 degrees. For our sector with a central angle of 100 degrees, this fraction is 100 divided by 360, which simplifies to 5/18 or approximately 0.278. This means the shaded region is exactly 5/18 of the circle's area. We can also calculate the actual area of the sector using the formula: area equals the angle in degrees divided by 360 degrees, multiplied by pi r squared. This problem demonstrates how geometric relationships can be expressed as simple fractions.