Question 10

The area of the rectangular region is approximately 300 percent of the area of the circular region.

The relationship between the areas indicates that the area of the rectangular region is significantly larger compared to the area of the circular region, specifically around 300 percent.

A) 33%

This option is incorrect as it underestimates the area of the rectangular region relative to the circular region. Since the shaded region is considerably larger, the ratio cannot be as low as 33%.

B) 75%

This choice also fails to accurately reflect the size of the rectangular region in relation to the circular region. A percentage of 75% suggests a closer proximity in size, which is not supported by the given information.

C) 100%

While this option suggests that the areas are equal, it does not account for the stated relationship where the area of the rectangular region is much larger than that of the circular region. Therefore, this option is incorrect.

D) 150%

Although this option implies that the rectangular region is larger than the circular region, it still falls short of the actual percentage. The difference in area is more substantial than 150%, making this choice incorrect.

E) 300%

This option is correct as it accurately represents the substantial difference in area between the rectangular and circular regions. Given that the area of the circular region is only about 50 percent of the shaded region, and the rectangular region is larger, 300 percent is the most reasonable estimate.

Conclusion

The correct answer, 300%, reflects the significant size difference between the rectangular and circular regions. All other options underestimate the area of the rectangular region, failing to recognize the true proportional relationship established in the question. Thus, option E is the only accurate choice based on the context provided.