Circle 1, circle 2, and circle 3 have the same center and have radii, respectively, of r1 cm, r2 cm, r3 cm, where r1 < r2 < r3. let a1 be the area of circle 1, let a2 be the area of the region within circle 2 and outside circle 1, and let a3 be the area of the region within circle 3 and outside circle 2, where all areas are in cm2. what are the values of \small \frac{a_{1}}{a_{2}} and \small \frac{a_{2}}{a_{3}} ?

The first area is simply the are of the innermost circle, so we have

Then, the region inside circle 2 and outside circle 1 is the difference between the areas of these circles:

By the same logic, we have

So, the ratios are

And similarly

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

42

step-by-step explanation: