Question

Which of the following statements correctly analyzes the error made by the student regarding the area of the circle?

A. The student underestimated the area of the circle because 1,090 cm² is smaller than the actual area.
B. The student overestimated the area of the circle because 1,090 cm² is larger than the actual area.
C. The student's error cannot be determined without knowing the actual area of the circle.
D. The student's error cannot be determined without knowing the radius or diameter of the circle.

Answer 1

The student overestimated the area of the circle because 1,090 cm² is larger than the actual area.

Step-by-step explanation:

The student overestimated the area of the circle because 1,090 cm² is larger than the actual area.

To analyze the error, we can refer to the given information: A circle within a square has an area smaller than that of the surrounding square, but larger than half the square area. The square has an area of a², and three-quarters of this is 3a², which is approximately equal to πr².

Since the student's calculation of the area is given as 1,090 cm², which is larger than the actual area, it can be concluded that the student overestimated the area of the circle.