Question
The area of circle 1 is 6 square units. The area of circle 2 is 7 square units.
Which of these statements is true about the circumferences of the circles?
Which of these statements is true about the circumferences of the circles?
Answers
GPT 3.5
Since the area of a circle is determined by the formula A = πr^2, where A is the area and r is the radius, we can find the radius of each circle.
For circle 1, with an area of 6 square units:
6 = πr^2
r^2 = 6/π
r ≈ √(6/π) ≈ 1.29 units
For circle 2, with an area of 7 square units:
7 = πr^2
r^2 = 7/π
r ≈ √(7/π) ≈ 1.49 units
Since the radius of circle 2 is larger than the radius of circle 1, the circumference of circle 2 is longer than the circumference of circle 1. Therefore, the statement "The circumference of circle 2 is longer than the circumference of circle 1" is true.
For circle 1, with an area of 6 square units:
6 = πr^2
r^2 = 6/π
r ≈ √(6/π) ≈ 1.29 units
For circle 2, with an area of 7 square units:
7 = πr^2
r^2 = 7/π
r ≈ √(7/π) ≈ 1.49 units
Since the radius of circle 2 is larger than the radius of circle 1, the circumference of circle 2 is longer than the circumference of circle 1. Therefore, the statement "The circumference of circle 2 is longer than the circumference of circle 1" is true.