## anonymous one year ago Water Runs into a conical tank at the rate of 3 feet^3/min. the tank stands pointing down and has a height of 15ft and a base radius of 4ft. How fast is the water level rising when the water is 8 feet deep.

1. anonymous

|dw:1443496421968:dw|

2. anonymous

not sure where to go from there

3. Vocaloid

|dw:1443496845151:dw| first step is to calculate r' (the value I marked), do you know how to do that?

4. anonymous

yea i think i do its, is this right ? $\frac{ r }{ h } = \frac{ 4 }{ 15 }$ $r = \frac{ 4h }{ 15 }$

5. Vocaloid

almost, we want the radius when h = 8, so you can plug in h = 8 into your proportion

6. anonymous

32/15 = 2.1333

7. Vocaloid

uh, lets leave it as a fraction for now (32/15) now, we just figured out that r = 4h/15, we can substitute that into the volume equation

8. Vocaloid

V = (1/3)(pi)(r^2)(h) = (1/3)(pi)(4h/15)^2*(h) now differentiate that with respect to h

9. Vocaloid

*with respect to t

10. anonymous

okay so $V = \frac{ 1 }{ 3 } \pi (\frac{ 32 }{ 15 }) ^2 h$

11. Vocaloid

actually, forget 32/15, we don't really need that (my mistake)

12. Vocaloid

|dw:1443497509872:dw|

13. anonymous

wait so do we treat the r in the function as a constant = to 32/15 ?

14. anonymous

ah i see okay

15. Vocaloid

right, we re-wrote r in terms of h, so we've already accounted for r (since r changes proportionally to h)

16. anonymous

so dv/dt = 2pi/3 (4h/15) h dh/dt ?

17. anonymous

is that right?

18. Vocaloid

not quite

19. Vocaloid

|dw:1443497761147:dw|

20. Vocaloid

then plug in h = 8 and dv/dt = 3

21. anonymous

wait why is h cubed, and also i thought it was 4h/15 not 4/15

22. Vocaloid

|dw:1443498112065:dw|

23. Vocaloid

24. anonymous

:P thats useful

25. anonymous

okay and where did the 1/3 go?

26. anonymous

okay nvm i see

27. anonymous

the power rule for the h^3 canceled it out

28. Vocaloid

29. Vocaloid

yeah that

30. anonymous

yep and the answer is .2098

31. anonymous

okay thank you very much!!!

32. Vocaloid

would be best to write it as a fraction in terms of pi, but yeah