The radius of a right circular cone is increasing at a rate of 1.6 in/s while its height is decreasing at a rate of 2.2 in/s. At what rate is the volume of the cone changing when the radius is 135 in. and the height is 135 in.

Step-by-step explanation:

let radius=r

height=h

dr/dt=1.6 in/s

dh/dt=-2.2 in/s

volume v=1/3 πr²h

dv/dt=1/3 π[h*2r×dr/dt+r²×dh/dt]

when r=135 in

h=135 in

dv/dt=1/3 π[2×135×135×1.6+135²×(-2.2)]

=1/3 π[135²(3.2-2.2)]

=1/3π135²×1

=6075 π in³/s

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